Answered step by step
Verified Expert Solution
Question
1 Approved Answer
I need help doing Present Value. Must use all 3 files to answer the questions. Direction: The first 5 pages will teach you about the
I need help doing Present Value. Must use all 3 files to answer the questions.
Direction: The first 5 pages will teach you about the basics of the present value calculation. Following are three scenarios/questions to be answered on the answer sheet and turned in class. Let's Learn Some Present Value!!! Let's assume that Sim Bhullar, a rookie center from NMSU, is offered a 5-year guaranteed contract totaling $1,000,000by Sacramento Kings. But the new team gives him two choices. He can get paid either: (1) $950,000 right now. OR (2) $200,000 at the end of each year for the next 5 years (Interest rate is 2% at the time). Although a layman may think that he should take Choice (2) because the total amount is $1 million compared to Choice (1)'s $950,000, having been educated at NMSU (albeit only 2 years) Sim Bhullar knows that he needs to consider the time value of money (or maybe he doesn't. He played 3 games for the Kings and is unemployed now). Time Value of Money Money today and money tomorrow can't be directly compared because of factors such as inflation and opportunity costs such as interest. Even without inflation and interest, people would rather have $1 more today than $1 more tomorrow. Sim Bhullar needs to think like a banker. He needs to pay close attention to the interest rate that banks use to exchange money today and money tomorrow. Interest rate allows us to convert the value of money today into the value of money tomorrow, and vice versa. If you put money in a bank today, the interest rate determines how much money you'll have in the future: - If you put $100 in the bank today and don't touch it and the interest rate is 5%, then in a year you'll have $105, your $100 principal plus $5 interest. If you borrow money from a bank today, the interest rate determines how much money you'll owe them in the future. - If you borrow $100 from the bank today and the interest rate is 5%, then in a year you'll owe them $105. In economics and accounting terms, this means that $100 is the PRESENT VALUE of getting $105 in one year when the interest rate is 5%. (Also $105 is the FUTURE VALUE of investing $100 for a year when the interest rate is 5%.) Present value is the value today of one or more future payments. It allows us to translate money tomorrow into money today. The formula for present value of a lump sum (Lump sum means all at once): PV = lump amount (1+interest rate)n where n denotes the end of n years. For example, - the present value of getting $100 one year from now if the interest rate is 5%: PV = 100 / (1+.05) 1 = 100 / 1.05 = 95.24 This also means that if you put $95.24 in the bank now at a 5% interest rate, in one year you'll have $100. - The present value of getting $100 TWO years from now if the interest rate is 5%: PV= 100 / (1+.05) 2 = 100 / 1.1025 = 90.70 This also means that if you put $90.70 in the bank now at a 5% interest rate, in two years you'll have $100. - Finally, the present value of getting $100 one hundred years from now if the interest rate is 5%: PV= 100 / (1+.05) 100 = 100 / 131.50 = 0.766666.... If you put 76 cents in the bank now at 5% interest and don't touch it for 100 years, you'll have $100 in 100 years. How? Because of the compounding interest. At a 5% interest rate, your $100 in the bank will earn interest of $5 (100 x 5%). In the second year, you don't earn interest of $5, you earn $5.25 (105 x 5%). Let's go back to Sim Bhullar's contract. What is the present value of $200,000 at the end of each year for the next 5 years? You can do the present value of a lump sum 5 times to get the PV, OR you can use a formula for the present value of an annuity (a series of equal payments for a period of time): PV = annuity amount / [(1- (1/(1+interest rate)n)] 1 PV =annuity amount x ( 1 ( 1+ interest rate )n ) interest rate 1 PV =200,000 x( PV =200,000 x( 1 1.104081 ) .02 10.905731 ) .02 PV =200,000 x( 4.71346) PV = $942,692 (There could be rounding errors) That's a lot of manual calculations! Thankfully, you can either use present value tables or your financial calculator. For the purpose of this class, we will use the tables. The excel file for this assignment has four tables in four different tabs. The first and second tabs have the factors for a lump sum amount. The third and fourth tabs have the factors for annuities. For the to Sim Bhullar example, look at Table 2a, find the factor for 5 periods and 2%. The factor is 4.713 (rounded), which is what we have from the manual calculation. Should to Sim Bhullar take the $950,000 today or $200,000 a year for the next 5 years? According to the present value calculation using 2% interest rate, he should take the $950,000 a year for the next 5 years, assuming that the interest rate is 2%. Remember: - Present value of a lump sum (Table 1a and 1b) calculates the present value of one - payment in the nth year with an interest rate of r. Present value of an annuity (Table 2a and 2b) calculates the present value of multiple payments of the same amount for the n number of years with an interest rate of r. For more information, read the textbook pages 448 to 455 (or look up Wikipedia). Now on to the problems. What's my monthly payment? If you are looking at purchasing a car, you ultimately come to a point when you ask the question, what's my monthly payment going to be? For most people, the monthly payment number comes from a black box where the numbers are magically calculated. In reality, the payment calculator is a simple present value calculation. Try this on your own. Go to audiusa.com. Click on the \"Models.\" You feel like A4 is a good compromise of practicality and luxury. Click on 2017 A4. Click on \"Build.\" The standard features are adequate for the Premium trim. Click continue. Since it doesn't snow in Southern New Mexico, you don't care for all-wheel drive. Choose the frontwheel drive starting at $37,300. You don't care for a metallic paint exterior or any of the options. The price at the top should still read $37,300 (it doesn't matter if it doesn't). Now, click the \"Estimate Payment\" tab on the right. Look on the right for \"Finance\" part. Change the term to 36 months. (A4 Sedan, Premium 2.0 TFSI, Seven-spped S tronic dual-clutch). The monthly payment amount will now read $1016.01. How did they come up with that? The other information reads that it is based on the amount financed as $34,465, 36 months, 3.9% annual APR, and $3,730 down payment and zero trade-in. So we use 36 periods and, for the interest rate, divide 3.9% by 12, which gives you 0.325%. This is an important point. When you look up PV tables, be aware that periods and interest rates have to be for the same period length. In other words, if you use years as periods, you use annual interest rate. If you use months as periods, you need to divide the annual interest rate by 12. When we talk about interest rates, they are always annual interest rates. PV of annuity = Payment x PV annuity factor $34,465 = Payment x (Look up PV Annuity Detailed Table2b: 36 periods = __________ x and 0.325%) $34,465 33.921854 Where did we see $1016.01 before? Estimated monthly payment! Basically, the present value of monthly payments will equal the MSRP. The car dealerships are basically collecting interest on the payments. In other words, there's no difference between a dealership getting paid a lump sum cash amount of $34,465and putting it into a bank collecting 3.9% interest or alternatively collecting monthly payments of $1016.01 for 36 months. When it comes for your time to buy a car, and you have a choice between financing and buying with cash, it really comes down to this: Can you earn interest at a higher rate than the interest for financing? If you can finance at 0.9%, and you can also earn 1.2% on your savings account, you should put the cash into your savings account and make monthly payments. If you don't have the cash or if your investment option yields less than 0.9%, you're stuck with paying 0.9% annual interest. Buy or Lease? Congratulations! Imagine yourself as a college graduate and you have become a Big 4 auditor. To celebrate, you decided to buy a new Audi A4: After building your car, let's say that the MSRP for your Audi is $38,000. Now you have a decision to make: Choice (1): Lease the car for 36 months Choice (2): Buy the car with cash out right (because you have so much cash just lying around) and sell it after 36 months. Detailed terms are: (A) Leasing: $4,927 amount due at signing $3,800 Down payment $432.60 monthly payment (B) Buying: $38,000 sales price $14,000 resale value at the end of 36 months Do the following calculations. Assume an interest rate of 1%, which is about the best you can do in savings accounts today: Leasing: (1) Initial costs: Down payment + cash due at signing = _________________ (2) Monthly payment (Use PV annuity detailed tab): 432.60 x PV annuity factor (36 periods, 1%/12=.083. Use 0.08%) = Total costs to lease (add (1) and (2)) _________________ = _________________ Buying: Initial costs: Sales Price = _________________ Resale value x PV lump sum factor (36 periods, 0.08%) = (________________) = _________________ Resale value (Use PV detailed tab): Total costs to buy Notice that for the buying option, we just assumed that you have the cash to pay for the Audi outright. It wouldn't have made any difference had we used monthly payments, because the present value of the monthly payments equals the sales price of the car anyway. So should you buy or lease (solely based on which is cheaper)? Circle: Buy Lease In real life, your decision comes down to whether you still want to keep the car longer than the lease term (usually 36 months). Also an important factor is how much you think you will be able to sell the car for in the future. Mortgage Payments to Pay Extra or Not You have found a house you want to purchase in Las Cruces at 2651 Sunset Pl, Las Cruces, NM 88011. The house is listed on Zillow as $159,900. With 20% down ($31,980) at the 30 year fixed interest, the monthly payment is $614. (1) Find what monthly interest rate Zillow is using the Table 2b: Answer: Between __________ % and ____________% (2) Practicing using the Excel program to solve PV calculations. a. Find the interest rate: In any cell, type =rate(. You now need to enter the following: Nper: number of periods Pmt: Amount of payment PV: present value [FV]: [ ] means this value is optional. This usually is not needed. Future Value [type]: Beginning of the month or end of the month. Default is end of the month (I think). [guess]: I've never used this before So type: =rate(360, -614, (159900-31980)), meaning 360 months, $614 payment, $127,920 financed (159900-31980). You have to put a negative sign either before the payment number or the present value number, otherwise you will get an error message. Click on one of the decimal buttons to so you see that it's not 0%. Answer: ______________% Monthly (show at least 7 digits after 0.) ______________ % Annual (show at least 5 digits after 0.) b. Using the monthly rate you got from (2)a, calculate the PV. The more digits you use for the more accurate the present value will be. Type in a cell =pv(, then type in the necessary numbers. For rate, you need to use the non-percentage number (for example, 0.04 instead of 4%) or put a % (for example, 4%). You should get the amount you are financing to buy the house (price minus down payment) c. Using the rate and the amount of financing, calculate the monthly payment. Type in a cell =pmt( then type in the necessary numbers. You should get t$614. (3) Make a mortgage amortization schedule. Start on a new worksheet a. Starting in cell B2 and ending in G2, label the six columns as periods, payment, additional payment, interest, principle paid, and principle. b. Under the Principle in period 0 (cell G3), put $127920. c. In the periods column, starting on B3 down to B363 put 0, 1, 2, down to 360. (after typing in 0,1,2, highlight the three cells and drag down until you have 360) d. In the payment column, in C4 (leave period 0 blank) put $614 starting on the period 1 row down to period 360. Drag down to 360 or double click the right lower corner of the cell. All cells under payment should be $614. e. Leave additional payment column blank for now. f. In the interest column on period 1 row (E4), type (or click after =) =G3* then the monthly rate you calculated above. Put as many digits. It should read $431.15. g. Under Principle paid column in period 1 (F4), type =C4+D4-E4 h. Under Principle in period 1 (G4), type =G3-F4 i. Highlight the period 1 interest, principle paid, and principle (E4 to G4), and drag down to period 360 or double click on the lower right corner of the 3 highlighted cells. Notice that at the end of period 360, the principle must have been paid off. Now put $86 in the additional payment column starting from period 1 to period 360, because you want to pay $700 even every month instead of $614. You'll notice that if you pay just $86 more every month, you will have paid off the mortgage after 285 months (23 years and 8 months) instead of 360 months (30 years and 0 month). Question: If you pay $386 more every month ($1,000 total payment even), after how many years and months will you have paid off the mortgage? ANSWER: ____________ years ___________ months Type you answers in the answer sheet file and print out a hard copy to turn in. Name:____________________ Leasing: (1) Initial costs: Down payment + cash due at signing = _________________ (2) Monthly payment (Use PV annuity detailed tab): 432.60 x PV annuity factor (36 periods, 1%/12=.083. Use 0.08%) = Total costs to lease (add (1) and (2)) _________________ = _________________ Buying: Initial costs: Sales Price = _________________ Resale value x PV lump sum factor (36 periods, 0.08%) = (________________) = _________________ Resale value (Use PV detailed tab): Total costs to buy So should you buy or lease (solely based on which is cheaper)? Circle: Buy Lease Mortgage Payments to Pay Extra or Not (1) Find what monthly interest rate Zillow is using the Table 2b: Answer: Between __________ % and ____________% (2) Practicing using the Excel program to solve PV calculations. Answer: ______________% Monthly (show at least 7 digits after 0.) ______________ % Annual (show at least 5 digits after 0.) (3) If you pay $386 more every month ($1,000 total payment even), after how many years and months will you have paid off the mortgage? (4) ANSWER: ____________ years ___________ months Number of Periods = Interest rate per period 1% 2% 1 0.990 0.980 2 0.980 0.961 3 0.971 0.942 4 0.961 0.924 5 0.951 0.906 6 0.942 0.888 7 0.933 0.871 8 0.923 0.853 9 0.914 0.837 10 0.905 0.820 11 0.896 0.804 12 0.887 0.788 13 0.879 0.773 14 0.870 0.758 15 0.861 0.743 16 0.853 0.728 17 0.844 0.714 18 0.836 0.700 19 0.828 0.686 20 0.820 0.673 21 0.811 0.660 22 0.803 0.647 23 0.795 0.634 24 0.788 0.622 25 0.780 0.610 26 0.772 0.598 27 0.764 0.586 28 0.757 0.574 29 0.749 0.563 30 0.742 0.552 31 0.735 0.541 32 0.727 0.531 33 0.720 0.520 34 0.713 0.510 35 0.706 0.500 36 0.699 0.490 37 0.692 0.481 38 0.685 0.471 39 0.678 0.462 40 0.672 0.453 3% 0.971 0.943 0.915 0.888 0.863 0.837 0.813 0.789 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.623 0.605 0.587 0.570 0.554 0.538 0.522 0.507 0.492 0.478 0.464 0.450 0.437 0.424 0.412 0.400 0.388 0.377 0.366 0.355 0.345 0.335 0.325 0.316 0.307 4% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456 0.439 0.422 0.406 0.390 0.375 0.361 0.347 0.333 0.321 0.308 0.296 0.285 0.274 0.264 0.253 0.244 0.234 0.225 0.217 0.208 5% 0.952 0.907 0.864 0.823 0.784 0.746 0.711 0.677 0.645 0.614 0.585 0.557 0.530 0.505 0.481 0.458 0.436 0.416 0.396 0.377 0.359 0.342 0.326 0.310 0.295 0.281 0.268 0.255 0.243 0.231 0.220 0.210 0.200 0.190 0.181 0.173 0.164 0.157 0.149 0.142 6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.294 0.278 0.262 0.247 0.233 0.220 0.207 0.196 0.185 0.174 0.164 0.155 0.146 0.138 0.130 0.123 0.116 0.109 0.103 0.097 7% 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 0.388 0.362 0.339 0.317 0.296 0.277 0.258 0.242 0.226 0.211 0.197 0.184 0.172 0.161 0.150 0.141 0.131 0.123 0.115 0.107 0.100 0.094 0.088 0.082 0.076 0.071 0.067 8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 0.199 0.184 0.170 0.158 0.146 0.135 0.125 0.116 0.107 0.099 0.092 0.085 0.079 0.073 0.068 0.063 0.058 0.054 0.050 0.046 9% 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178 0.164 0.150 0.138 0.126 0.116 0.106 0.098 0.090 0.082 0.075 0.069 0.063 0.058 0.053 0.049 0.045 0.041 0.038 0.035 0.032 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.135 0.123 0.112 0.102 0.092 0.084 0.076 0.069 0.063 0.057 0.052 0.047 0.043 0.039 0.036 0.032 0.029 0.027 0.024 0.022 11% 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124 0.112 0.101 0.091 0.082 0.074 0.066 0.060 0.054 0.048 0.044 0.039 0.035 0.032 0.029 0.026 0.023 0.021 0.019 0.017 0.015 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 0.093 0.083 0.074 0.066 0.059 0.053 0.047 0.042 0.037 0.033 0.030 0.027 0.024 0.021 0.019 0.017 0.015 0.013 0.012 0.011 13% 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295 0.261 0.231 0.204 0.181 0.160 0.141 0.125 0.111 0.098 0.087 0.077 0.068 0.060 0.053 0.047 0.042 0.037 0.033 0.029 0.026 0.023 0.020 0.018 0.016 0.014 0.012 0.011 0.010 0.009 0.008 14% 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.064 0.056 0.049 0.043 0.038 0.033 0.029 0.026 0.022 0.020 0.017 0.015 0.013 0.012 0.010 0.009 0.008 0.007 0.006 0.005 15% 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 0.215 0.187 0.163 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.053 0.046 0.040 0.035 0.030 0.026 0.023 0.020 0.017 0.015 0.013 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.004 Number of Periods Interest rate per period 0.05% 0.06% 1 1.000 0.999 2 0.999 0.999 3 0.999 0.998 4 0.998 0.998 5 0.998 0.997 6 0.997 0.996 7 0.997 0.996 8 0.996 0.995 9 0.996 0.995 10 0.995 0.994 11 0.995 0.993 12 0.994 0.993 13 0.994 0.992 14 0.993 0.992 15 0.993 0.991 16 0.992 0.990 17 0.992 0.990 18 0.991 0.989 19 0.991 0.989 20 0.990 0.988 21 0.990 0.987 22 0.989 0.987 23 0.989 0.986 24 0.988 0.986 25 0.988 0.985 26 0.987 0.985 27 0.987 0.984 28 0.986 0.983 29 0.986 0.983 30 0.985 0.982 31 0.985 0.982 32 0.984 0.981 33 0.984 0.980 34 0.983 0.980 35 0.983 0.979 36 0.982 0.979 37 0.982 0.978 38 0.981 0.977 39 0.981 0.977 40 0.980 0.976 0.07% 0.999 0.999 0.998 0.997 0.997 0.996 0.995 0.994 0.994 0.993 0.992 0.992 0.991 0.990 0.990 0.989 0.988 0.987 0.987 0.986 0.985 0.985 0.984 0.983 0.983 0.982 0.981 0.981 0.980 0.979 0.979 0.978 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.08% 0.999 0.998 0.998 0.997 0.996 0.995 0.994 0.994 0.993 0.992 0.991 0.990 0.990 0.989 0.988 0.987 0.986 0.986 0.985 0.984 0.983 0.983 0.982 0.981 0.980 0.979 0.979 0.978 0.977 0.976 0.976 0.975 0.974 0.973 0.972 0.972 0.971 0.970 0.969 0.969 0.09% 0.999 0.998 0.997 0.996 0.996 0.995 0.994 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.987 0.986 0.985 0.984 0.983 0.982 0.981 0.980 0.980 0.979 0.978 0.977 0.976 0.975 0.974 0.973 0.972 0.972 0.971 0.970 0.969 0.968 0.967 0.966 0.966 0.965 0.10% 0.999 0.998 0.997 0.996 0.995 0.994 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983 0.982 0.981 0.980 0.979 0.978 0.977 0.976 0.975 0.974 0.973 0.972 0.971 0.970 0.969 0.969 0.968 0.967 0.966 0.965 0.964 0.963 0.962 0.961 0.11% 0.999 0.998 0.997 0.996 0.995 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983 0.981 0.980 0.979 0.978 0.977 0.976 0.975 0.974 0.973 0.972 0.971 0.970 0.969 0.968 0.966 0.965 0.964 0.963 0.962 0.961 0.960 0.959 0.958 0.957 0.12% 0.999 0.998 0.996 0.995 0.994 0.993 0.992 0.990 0.989 0.988 0.987 0.986 0.985 0.983 0.982 0.981 0.980 0.979 0.977 0.976 0.975 0.974 0.973 0.972 0.970 0.969 0.968 0.967 0.966 0.965 0.964 0.962 0.961 0.960 0.959 0.958 0.957 0.955 0.954 0.953 0.13% 0.999 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.988 0.987 0.986 0.985 0.983 0.982 0.981 0.979 0.978 0.977 0.976 0.974 0.973 0.972 0.971 0.969 0.968 0.967 0.966 0.964 0.963 0.962 0.961 0.959 0.958 0.957 0.956 0.954 0.953 0.952 0.951 0.949 0.14% 0.999 0.997 0.996 0.994 0.993 0.992 0.990 0.989 0.987 0.986 0.985 0.983 0.982 0.981 0.979 0.978 0.976 0.975 0.974 0.972 0.971 0.970 0.968 0.967 0.966 0.964 0.963 0.962 0.960 0.959 0.958 0.956 0.955 0.954 0.952 0.951 0.950 0.948 0.947 0.946 0.15% 0.999 0.997 0.996 0.994 0.993 0.991 0.990 0.988 0.987 0.985 0.984 0.982 0.981 0.979 0.978 0.976 0.975 0.973 0.972 0.970 0.969 0.968 0.966 0.965 0.963 0.962 0.960 0.959 0.957 0.956 0.955 0.953 0.952 0.950 0.949 0.947 0.946 0.945 0.943 0.942 0.16% 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.981 0.979 0.978 0.976 0.975 0.973 0.972 0.970 0.969 0.967 0.965 0.964 0.962 0.961 0.959 0.958 0.956 0.955 0.953 0.952 0.950 0.949 0.947 0.946 0.944 0.943 0.941 0.940 0.938 0.17% 0.998 0.997 0.995 0.993 0.992 0.990 0.988 0.987 0.985 0.983 0.981 0.980 0.978 0.977 0.975 0.973 0.972 0.970 0.968 0.967 0.965 0.963 0.962 0.960 0.958 0.957 0.955 0.954 0.952 0.950 0.949 0.947 0.945 0.944 0.942 0.941 0.939 0.937 0.936 0.934 0.18% 0.998 0.996 0.995 0.993 0.991 0.989 0.987 0.986 0.984 0.982 0.980 0.979 0.977 0.975 0.973 0.972 0.970 0.968 0.966 0.965 0.963 0.961 0.959 0.958 0.956 0.954 0.953 0.951 0.949 0.947 0.946 0.944 0.942 0.941 0.939 0.937 0.936 0.934 0.932 0.931 0.19% 0.998 0.996 0.994 0.992 0.991 0.989 0.987 0.985 0.983 0.981 0.979 0.977 0.976 0.974 0.972 0.970 0.968 0.966 0.965 0.963 0.961 0.959 0.957 0.955 0.954 0.952 0.950 0.948 0.946 0.945 0.943 0.941 0.939 0.937 0.936 0.934 0.932 0.930 0.929 0.927 0.20% 0.998 0.996 0.994 0.992 0.990 0.988 0.986 0.984 0.982 0.980 0.978 0.976 0.974 0.972 0.970 0.969 0.967 0.965 0.963 0.961 0.959 0.957 0.955 0.953 0.951 0.949 0.947 0.946 0.944 0.942 0.940 0.938 0.936 0.934 0.932 0.931 0.929 0.927 0.925 0.923 0.21% 0.998 0.996 0.994 0.992 0.990 0.987 0.985 0.983 0.981 0.979 0.977 0.975 0.973 0.971 0.969 0.967 0.965 0.963 0.961 0.959 0.957 0.955 0.953 0.951 0.949 0.947 0.945 0.943 0.941 0.939 0.937 0.935 0.933 0.931 0.929 0.927 0.925 0.923 0.921 0.920 0.22% 0.998 0.996 0.993 0.991 0.989 0.987 0.985 0.983 0.980 0.978 0.976 0.974 0.972 0.970 0.968 0.965 0.963 0.961 0.959 0.957 0.955 0.953 0.951 0.949 0.947 0.944 0.942 0.940 0.938 0.936 0.934 0.932 0.930 0.928 0.926 0.924 0.922 0.920 0.918 0.916 0.23% 0.998 0.995 0.993 0.991 0.989 0.986 0.984 0.982 0.980 0.977 0.975 0.973 0.971 0.968 0.966 0.964 0.962 0.959 0.957 0.955 0.953 0.951 0.949 0.946 0.944 0.942 0.940 0.938 0.936 0.933 0.931 0.929 0.927 0.925 0.923 0.921 0.919 0.916 0.914 0.912 0.24% 0.998 0.995 0.993 0.990 0.988 0.986 0.983 0.981 0.979 0.976 0.974 0.972 0.969 0.967 0.965 0.962 0.960 0.958 0.955 0.953 0.951 0.949 0.946 0.944 0.942 0.940 0.937 0.935 0.933 0.931 0.928 0.926 0.924 0.922 0.920 0.917 0.915 0.913 0.911 0.909 0.25% 0.998 0.995 0.993 0.990 0.988 0.985 0.983 0.980 0.978 0.975 0.973 0.970 0.968 0.966 0.963 0.961 0.958 0.956 0.954 0.951 0.949 0.947 0.944 0.942 0.939 0.937 0.935 0.932 0.930 0.928 0.926 0.923 0.921 0.919 0.916 0.914 0.912 0.909 0.907 0.905 0.26% 0.997 0.995 0.992 0.990 0.987 0.985 0.982 0.979 0.977 0.974 0.972 0.969 0.967 0.964 0.962 0.959 0.957 0.954 0.952 0.949 0.947 0.944 0.942 0.940 0.937 0.935 0.932 0.930 0.927 0.925 0.923 0.920 0.918 0.915 0.913 0.911 0.908 0.906 0.904 0.901 0.27% 0.997 0.995 0.992 0.989 0.987 0.984 0.981 0.979 0.976 0.973 0.971 0.968 0.966 0.963 0.960 0.958 0.955 0.953 0.950 0.948 0.945 0.942 0.940 0.937 0.935 0.932 0.930 0.927 0.925 0.922 0.920 0.917 0.915 0.912 0.910 0.907 0.905 0.903 0.900 0.898 0.28% 0.997 0.994 0.992 0.989 0.986 0.983 0.981 0.978 0.975 0.972 0.970 0.967 0.964 0.962 0.959 0.956 0.954 0.951 0.948 0.946 0.943 0.940 0.938 0.935 0.932 0.930 0.927 0.925 0.922 0.920 0.917 0.914 0.912 0.909 0.907 0.904 0.902 0.899 0.897 0.894 0.29% 0.997 0.994 0.991 0.988 0.986 0.983 0.980 0.977 0.974 0.971 0.969 0.966 0.963 0.960 0.957 0.955 0.952 0.949 0.946 0.944 0.941 0.938 0.936 0.933 0.930 0.927 0.925 0.922 0.919 0.917 0.914 0.911 0.909 0.906 0.904 0.901 0.898 0.896 0.893 0.891 0.30% 0.997 0.994 0.991 0.988 0.985 0.982 0.979 0.976 0.973 0.970 0.968 0.965 0.962 0.959 0.956 0.953 0.950 0.948 0.945 0.942 0.939 0.936 0.933 0.931 0.928 0.925 0.922 0.920 0.917 0.914 0.911 0.909 0.906 0.903 0.900 0.898 0.895 0.892 0.890 0.887 0.31% 0.997 0.994 0.991 0.988 0.985 0.982 0.979 0.976 0.973 0.970 0.967 0.964 0.961 0.958 0.955 0.952 0.949 0.946 0.943 0.940 0.937 0.934 0.931 0.928 0.926 0.923 0.920 0.917 0.914 0.911 0.909 0.906 0.903 0.900 0.897 0.895 0.892 0.889 0.886 0.884 0.32% 0.997 0.994 0.990 0.987 0.984 0.981 0.978 0.975 0.972 0.969 0.965 0.962 0.959 0.956 0.953 0.950 0.947 0.944 0.941 0.938 0.935 0.932 0.929 0.926 0.923 0.920 0.917 0.914 0.912 0.909 0.906 0.903 0.900 0.897 0.894 0.891 0.889 0.886 0.883 0.880 0.33% 0.997 0.993 0.990 0.987 0.984 0.980 0.977 0.974 0.971 0.968 0.964 0.961 0.958 0.955 0.952 0.949 0.946 0.942 0.939 0.936 0.933 0.930 0.927 0.924 0.921 0.918 0.915 0.912 0.909 0.906 0.903 0.900 0.897 0.894 0.891 0.888 0.885 0.882 0.879 0.877 0.34% 0.997 0.993 0.990 0.987 0.983 0.980 0.977 0.973 0.970 0.967 0.963 0.960 0.957 0.954 0.950 0.947 0.944 0.941 0.938 0.934 0.931 0.928 0.925 0.922 0.919 0.916 0.912 0.909 0.906 0.903 0.900 0.897 0.894 0.891 0.888 0.885 0.882 0.879 0.876 0.873 0.35% 0.997 0.993 0.990 0.986 0.983 0.979 0.976 0.972 0.969 0.966 0.962 0.959 0.956 0.952 0.949 0.946 0.942 0.939 0.936 0.933 0.929 0.926 0.923 0.920 0.916 0.913 0.910 0.907 0.904 0.900 0.897 0.894 0.891 0.888 0.885 0.882 0.879 0.876 0.873 0.870 Number of Periods Interest rate per period 1% 2% 1 0.990 0.980 2 1.970 1.942 3 2.941 2.884 4 3.902 3.808 5 4.853 4.713 6 5.795 5.601 7 6.728 6.472 8 7.652 7.325 9 8.566 8.162 10 9.471 8.983 11 10.368 9.787 12 11.255 10.575 13 12.134 11.348 14 13.004 12.106 15 13.865 12.849 16 14.718 13.578 17 15.562 14.292 18 16.398 14.992 19 17.226 15.678 20 18.046 16.351 21 18.857 17.011 22 19.660 17.658 23 20.456 18.292 24 21.243 18.914 25 22.023 19.523 26 22.795 20.121 27 23.560 20.707 28 24.316 21.281 29 25.066 21.844 30 25.808 22.396 31 26.542 22.938 32 27.270 23.468 33 27.990 23.989 34 28.703 24.499 35 29.409 24.999 36 30.108 25.489 37 30.800 25.969 38 31.485 26.441 39 32.163 26.903 40 32.835 27.355 41 33.500 27.799 42 34.158 28.235 43 34.810 28.662 44 35.455 29.080 45 36.095 29.490 46 36.727 29.892 47 37.354 30.287 48 37.974 30.673 49 38.588 31.052 50 39.196 31.424 51 39.798 31.788 52 40.394 32.145 53 40.984 32.495 54 41.569 32.838 55 42.147 33.175 56 42.720 33.505 57 43.287 33.828 58 43.849 34.145 59 44.405 34.456 60 44.955 34.761 61 45.500 35.060 62 46.040 35.353 63 46.574 35.640 64 47.103 35.921 65 47.627 36.197 66 48.145 36.468 67 48.659 36.733 68 49.167 36.994 69 49.670 37.249 70 50.169 37.499 71 50.662 37.744 72 51.150 37.984 73 51.634 38.220 74 52.113 38.451 75 52.587 38.677 76 53.056 38.899 77 53.521 39.117 78 53.981 39.330 79 54.437 39.539 3% 0.971 1.913 2.829 3.717 4.580 5.417 6.230 7.020 7.786 8.530 9.253 9.954 10.635 11.296 11.938 12.561 13.166 13.754 14.324 14.877 15.415 15.937 16.444 16.936 17.413 17.877 18.327 18.764 19.188 19.600 20.000 20.389 20.766 21.132 21.487 21.832 22.167 22.492 22.808 23.115 23.412 23.701 23.982 24.254 24.519 24.775 25.025 25.267 25.502 25.730 25.951 26.166 26.375 26.578 26.774 26.965 27.151 27.331 27.506 27.676 27.840 28.000 28.156 28.306 28.453 28.595 28.733 28.867 28.997 29.123 29.246 29.365 29.481 29.593 29.702 29.808 29.910 30.010 30.107 4% 0.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 10.563 11.118 11.652 12.166 12.659 13.134 13.590 14.029 14.451 14.857 15.247 15.622 15.983 16.330 16.663 16.984 17.292 17.588 17.874 18.148 18.411 18.665 18.908 19.143 19.368 19.584 19.793 19.993 20.186 20.371 20.549 20.720 20.885 21.043 21.195 21.341 21.482 21.617 21.748 21.873 21.993 22.109 22.220 22.327 22.430 22.528 22.623 22.715 22.803 22.887 22.969 23.047 23.122 23.194 23.264 23.330 23.395 23.456 23.516 23.573 23.628 23.680 23.731 23.780 23.827 23.872 5% 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 16.374 16.547 16.711 16.868 17.017 17.159 17.294 17.423 17.546 17.663 17.774 17.880 17.981 18.077 18.169 18.256 18.339 18.418 18.493 18.565 18.633 18.699 18.761 18.820 18.876 18.929 18.980 19.029 19.075 19.119 19.161 19.201 19.239 19.275 19.310 19.343 19.374 19.404 19.432 19.459 19.485 19.509 19.533 19.555 19.576 6% 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.106 10.477 10.828 11.158 11.470 11.764 12.042 12.303 12.550 12.783 13.003 13.211 13.406 13.591 13.765 13.929 14.084 14.230 14.368 14.498 14.621 14.737 14.846 14.949 15.046 15.138 15.225 15.306 15.383 15.456 15.524 15.589 15.650 15.708 15.762 15.813 15.861 15.907 15.950 15.991 16.029 16.065 16.099 16.131 16.161 16.190 16.217 16.242 16.266 16.289 16.310 16.331 16.350 16.368 16.385 16.401 16.416 16.430 16.443 16.456 16.468 16.479 16.490 16.500 7% 0.935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.059 10.336 10.594 10.836 11.061 11.272 11.469 11.654 11.826 11.987 12.137 12.278 12.409 12.532 12.647 12.754 12.854 12.948 13.035 13.117 13.193 13.265 13.332 13.394 13.452 13.507 13.558 13.606 13.650 13.692 13.730 13.767 13.801 13.832 13.862 13.890 13.916 13.940 13.963 13.984 14.003 14.022 14.039 14.055 14.070 14.084 14.098 14.110 14.121 14.132 14.142 14.152 14.160 14.169 14.176 14.183 14.190 14.196 14.202 14.208 14.213 14.218 8% 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10.017 10.201 10.371 10.529 10.675 10.810 10.935 11.051 11.158 11.258 11.350 11.435 11.514 11.587 11.655 11.717 11.775 11.829 11.879 11.925 11.967 12.007 12.043 12.077 12.108 12.137 12.164 12.189 12.212 12.233 12.253 12.272 12.288 12.304 12.319 12.332 12.344 12.356 12.367 12.377 12.386 12.394 12.402 12.409 12.416 12.422 12.428 12.433 12.438 12.443 12.447 12.451 12.455 12.458 12.461 12.464 12.467 12.469 12.471 9% 0.917 1.759 2.531 3.240 3.890 4.486 5.033 5.535 5.995 6.418 6.805 7.161 7.487 7.786 8.061 8.313 8.544 8.756 8.950 9.129 9.292 9.442 9.580 9.707 9.823 9.929 10.027 10.116 10.198 10.274 10.343 10.406 10.464 10.518 10.567 10.612 10.653 10.691 10.726 10.757 10.787 10.813 10.838 10.861 10.881 10.900 10.918 10.934 10.948 10.962 10.974 10.985 10.996 11.005 11.014 11.022 11.029 11.036 11.042 11.048 11.053 11.058 11.062 11.066 11.070 11.073 11.077 11.079 11.082 11.084 11.087 11.089 11.091 11.092 11.094 11.095 11.097 11.098 11.099 10% 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 8.514 8.649 8.772 8.883 8.985 9.077 9.161 9.237 9.307 9.370 9.427 9.479 9.526 9.569 9.609 9.644 9.677 9.706 9.733 9.757 9.779 9.799 9.817 9.834 9.849 9.863 9.875 9.887 9.897 9.906 9.915 9.923 9.930 9.936 9.942 9.947 9.952 9.956 9.960 9.964 9.967 9.970 9.973 9.975 9.978 9.980 9.981 9.983 9.985 9.986 9.987 9.988 9.990 9.990 9.991 9.992 9.993 9.994 9.994 9.995 11% 0.901 1.713 2.444 3.102 3.696 4.231 4.712 5.146 5.537 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 7.839 7.963 8.075 8.176 8.266 8.348 8.422 8.488 8.548 8.602 8.650 8.694 8.733 8.769 8.801 8.829 8.855 8.879 8.900 8.919 8.936 8.951 8.965 8.977 8.989 8.999 9.008 9.016 9.024 9.030 9.036 9.042 9.047 9.051 9.055 9.058 9.062 9.065 9.067 9.070 9.072 9.074 9.075 9.077 9.078 9.079 9.081 9.082 9.083 9.083 9.084 9.085 9.085 9.086 9.086 9.087 9.087 9.088 9.088 9.088 9.089 12% 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 7.562 7.645 7.718 7.784 7.843 7.896 7.943 7.984 8.022 8.055 8.085 8.112 8.135 8.157 8.176 8.192 8.208 8.221 8.233 8.244 8.253 8.262 8.270 8.276 8.283 8.288 8.293 8.297 8.301 8.304 8.308 8.310 8.313 8.315 8.317 8.319 8.320 8.322 8.323 8.324 8.325 8.326 8.327 8.327 8.328 8.329 8.329 8.330 8.330 8.330 8.331 8.331 8.331 8.331 8.332 8.332 8.332 8.332 8.332 13% 0.885 1.668 2.361 2.974 3.517 3.998 4.423 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 6.729 6.840 6.938 7.025 7.102 7.170 7.230 7.283 7.330 7.372 7.409 7.441 7.470 7.496 7.518 7.538 7.556 7.572 7.586 7.598 7.609 7.618 7.627 7.634 7.641 7.647 7.652 7.657 7.661 7.664 7.668 7.671 7.673 7.675 7.677 7.679 7.680 7.682 7.683 7.684 7.685 7.686 7.687 7.687 7.688 7.688 7.689 7.689 7.690 7.690 7.690 7.690 7.691 7.691 7.691 7.691 7.691 7.691 7.692 7.692 7.692 7.692 7.692 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 6.687 6.743 6.792 6.835 6.873 6.906 6.935 6.961 6.983 7.003 7.020 7.035 7.048 7.060 7.070 7.079 7.087 7.094 7.100 7.105 7.110 7.114 7.117 7.120 7.123 7.126 7.128 7.130 7.131 7.133 7.134 7.135 7.136 7.137 7.138 7.138 7.139 7.139 7.140 7.140 7.140 7.141 7.141 7.141 7.141 7.142 7.142 7.142 7.142 7.142 7.142 7.142 7.142 7.142 7.142 7.143 7.143 7.143 7.143 15% 0.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 5.954 6.047 6.128 6.198 6.259 6.312 6.359 6.399 6.434 6.464 6.491 6.514 6.534 6.551 6.566 6.579 6.591 6.600 6.609 6.617 6.623 6.629 6.634 6.638 6.642 6.645 6.648 6.650 6.652 6.654 6.656 6.657 6.659 6.660 6.661 6.661 6.662 6.663 6.663 6.664 6.664 6.664 6.665 6.665 6.665 6.665 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.666 6.667 6.667 6.667 6.667 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 54.888 55.335 55.777 56.215 56.648 57.078 57.503 57.923 58.340 58.752 59.161 59.565 59.966 60.362 60.754 61.143 61.528 61.909 62.286 62.659 63.029 63.395 63.757 64.116 64.471 64.823 65.172 65.516 65.858 66.196 66.531 66.862 67.190 67.515 67.836 68.155 68.470 68.782 69.092 69.398 69.701 70.001 70.298 70.592 70.883 71.171 71.457 71.739 72.019 72.296 72.570 72.842 73.111 73.377 73.641 73.902 74.160 74.416 74.669 74.920 75.168 75.414 75.658 75.899 76.137 76.373 76.607 76.839 77.068 77.295 77.520 77.743 77.963 78.181 78.397 78.611 78.823 79.033 79.240 79.446 79.649 39.745 39.946 40.143 40.336 40.526 40.711 40.893 41.072 41.247 41.419 41.587 41.752 41.914 42.072 42.228 42.380 42.529 42.676 42.820 42.960 43.098 43.234 43.366 43.496 43.624 43.749 43.872 43.992 44.110 44.225 44.338 44.449 44.558 44.665 44.769 44.872 44.973 45.071 45.168 45.262 45.355 45.446 45.536 45.623 45.709 45.793 45.876 45.957 46.036 46.114 46.190 46.265 46.338 46.410 46.480 46.549 46.617 46.683 46.748 46.812 46.874 46.936 46.996 47.055 47.112 47.169 47.224 47.279 47.332 47.385 47.436 47.486 47.535 47.584 47.631 47.678 47.723 47.768 47.812 47.854 47.896 30.201 30.292 30.381 30.467 30.550 30.631 30.710 30.786 30.860 30.932 31.002 31.070 31.136 31.200 31.262 31.323 31.381 31.438 31.493 31.547 31.599 31.649 31.698 31.746 31.792 31.837 31.881 31.923 31.964 32.004 32.043 32.080 32.117 32.152 32.187 32.220 32.252 32.284 32.315 32.344 32.373 32.401 32.428 32.455 32.480 32.505 32.529 32.553 32.575 32.597 32.619 32.640 32.660 32.679 32.698 32.717 32.735 32.752 32.769 32.786 32.802 32.817 32.832 32.847 32.861 32.875 32.888 32.901 32.914 32.926 32.938 32.949 32.960 32.971 32.982 32.992 33.002 33.012 33.021 33.030 33.039 23.915 23.957 23.997 24.036 24.073 24.109 24.143 24.176 24.207 24.238 24.267 24.295 24.323 24.349 24.374 24.398 24.421 24.443 24.465 24.485 24.505 24.524 24.542 24.560 24.577 24.593 24.609 24.624 24.638 24.652 24.666 24.678 24.691 24.703 24.714 24.725 24.736 24.746 24.756 24.765 24.774 24.783 24.791 24.799 24.807 24.814 24.821 24.828 24.835 24.841 24.847 24.853 24.859 24.864 24.870 24.875 24.879 24.884 24.888 24.893 24.897 24.901 24.905 24.908 24.912 24.915 24.919 24.922 24.925 24.928 24.930 24.933 24.936 24.938 24.940 24.943 24.945 24.947 24.949 24.951 24.953 19.596 19.616 19.634 19.651 19.668 19.684 19.699 19.713 19.727 19.740 19.752 19.764 19.775 19.786 19.796 19.806 19.815 19.824 19.832 19.840 19.848 19.855 19.862 19.869 19.875 19.881 19.887 19.892 19.897 19.902 19.907 19.911 19.915 19.919 19.923 19.927 19.930 19.934 19.937 19.940 19.943 19.945 19.948 19.950 19.953 19.955 19.957 19.959 19.961 19.963 19.965 19.966 19.968 19.970 19.971 19.972 19.974 19.975 19.976 19.977 19.978 19.979 19.980 19.981 19.982 19.983 19.984 19.985 19.985 19.986 19.987 19.987 19.988 19.989 19.989 19.990 19.990 19.991 19.991 19.991 19.992 16.509 16.518 16.526 16.534 16.542 16.549 16.556 16.562 16.568 16.573 16.579 16.584 16.588 16.593 16.597 16.601 16.605 16.608 16.611 16.615 16.618 16.620 16.623 16.625 16.628 16.630 16.632 16.634 16.636 16.638 16.639 16.641 16.642 16.644 16.645 16.646 16.647 16.648 16.649 16.650 16.651 16.652 16.653 16.654 16.655 16.655 16.656 16.656 16.657 16.658 16.658 16.659 16.659 16.659 16.660 16.660 16.661 16.661 16.661 16.662 16.662 16.662 16.662 16.663 16.663 16.663 16.663 16.663 16.664 16.664 16.664 16.664 16.664 16.664 16.665 16.665 16.665 16.665 16.665 16.665 16.665 14.222 14.226 14.230 14.234 14.237 14.240 14.243 14.246 14.249 14.251 14.253 14.255 14.257 14.259 14.261 14.263 14.264 14.266 14.267 14.268 14.269 14.270 14.271 14.272 14.273 14.274 14.275 14.275 14.276 14.277 14.277 14.278 14.278 14.279 14.279 14.280 14.280 14.281 14.281 14.281 14.281 14.282 14.282 14.282 14.282 14.283 14.283 14.283 14.283 14.283 14.284 14.284 14.284 14.284 14.284 14.284 14.284 14.284 14.284 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 14.285 12.474 12.475 12.477 12.479 12.481 12.482 12.483 12.485 12.486 12.487 12.488 12.489 12.489 12.490 12.491 12.492 12.492 12.493 12.493 12.494 12.494 12.495 12.495 12.495 12.496 12.496 12.496 12.497 12.497 12.497 12.497 12.498 12.498 12.498 12.498 12.498 12.498 12.498 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.499 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 11.100 11.101 11.102 11.102 11.103 11.104 11.104 11.105 11.105 11.106 11.106 11.107 11.107 11.107 11.108 11.108 11.108 11.109 11.109 11.109 11.109 11.109 11.109 11.110 11.110 11.110 11.110 11.110 11.110 11.110 11.110 11.110 11.110 11.110 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 9.995 9.996 9.996 9.996 9.997 9.997 9.997 9.997 9.998 9.998 9.998 9.998 9.998 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 9.089 9.089 9.089 9.089 9.089 9.090 9.090 9.090 9.090 9.090 9.090 9.090 9.090 9.090 9.090 9.090 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 8.332 8.332 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 79.851 80.050 80.248 80.443 80.637 80.829 81.018 81.206 81.393 81.577 81.759 81.940 82.119 82.296 82.471 82.644 82.816 82.986 83.155 83.322 83.487 83.650 83.812 83.972 84.131 84.288 84.444 84.598 84.750 84.901 85.051 85.199 85.345 85.490 85.634 85.776 85.917 86.057 86.195 86.331 86.467 86.601 86.733 86.865 86.995 87.124 87.251 87.377 87.502 87.626 87.748 87.870 87.990 88.109 88.227 88.343 88.459 88.573 88.686 88.798 88.909 89.019 89.127 89.235 89.342 89.447 89.552 89.655 89.758 89.859 89.959 90.059 90.157 90.255 90.351 90.447 90.541 90.635 90.728 90.819 90.910 47.938 47.978 48.018 48.057 48.095 48.132 48.169 48.205 48.240 48.274 48.308 48.341 48.374 48.406 48.437 48.468 48.498 48.527 48.556 48.584 48.612 48.639 48.666 48.692 48.718 48.743 48.768 48.792 48.815 48.839 48.861 48.884 48.906 48.927 48.948 48.969 48.989 49.009 49.028 49.047 49.066 49.084 49.102 49.120 49.137 49.154 49.171 49.187 49.203 49.218 49.234 49.249 49.264 49.278 49.292 49.306 49.320 49.333 49.346 49.359 49.371 49.384 49.396 49.408 49.419 49.431 49.442 49.453 49.464 49.474 49.484 49.494 49.504 49.514 49.524 49.533 49.542 49.551 49.560 49.569 49.577 33.048 33.056 33.064 33.072 33.079 33.087 33.094 33.101 33.108 33.114 33.121 33.127 33.133 33.139 33.144 33.150 33.155 33.160 33.165 33.170 33.175 33.180 33.184 33.189 33.193 33.197 33.201 33.205 33.208 33.212 33.216 33.219 33.222 33.226 33.229 33.232 33.235 33.238 33.240 33.243 33.246 33.248 33.251 33.253 33.255 33.258 33.260 33.262 33.264 33.266 33.268 33.270 33.272 33.274 33.275 33.277 33.279 33.280 33.282 33.283 33.285 33.286 33.288 33.289 33.290 33.291 33.293 33.294 33.295 33.296 33.297 33.298 33.299 33.300 33.301 33.302 33.303 33.304 33.305 33.306 33.306 24.955 24.956 24.958 24.960 24.961 24.963 24.964 24.966 24.967 24.968 24.969 24.971 24.972 24.973 24.974 24.975 24.976 24.977 24.978 24.979 24.979 24.980 24.981 24.982 24.982 24.983 24.984 24.984 24.985 24.985 24.986 24.987 24.987 24.988 24.988 24.989 24.989 24.989 24.990 24.990 24.991 24.991 24.991 24.992 24.992 24.992 24.993 24.993 24.993 24.993 24.994 24.994 24.994 24.994 24.995 24.995 24.995 24.995 24.995 24.996 24.996 24.996 24.996 24.996 24.996 24.996 24.997 24.997 24.997 24.997 24.997 24.997 24.997 24.997 24.998 24.998 24.998 24.998 24.998 24.998 24.998 19.992 19.993 19.993 19.993 19.994 19.994 19.994 19.994 19.995 19.995 19.995 19.995 19.996 19.996 19.996 19.996 19.996 19.997 19.997 19.997 19.997 19.997 19.997 19.997 19.998 19.998 19.998 19.998 19.998 19.998 19.998 19.998 19.998 19.998 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 19.999 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 16.665 16.665 16.665 16.665 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.666 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 14.285 14.285 14.285 14.285 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 91.000 91.089 91.178 91.265 91.351 91.437 91.522 91.606 91.689 91.771 91.853 91.933 92.013 92.092 92.171 92.248 92.325 92.401 92.476 92.551 92.624 92.697 92.770 92.841 92.912 92.982 93.052 93.121 93.189 93.256 93.323 93.389 93.454 93.519 93.583 93.647 93.710 93.772 93.834 93.895 93.955 94.015 94.074 94.133 94.191 94.249 94.306 94.362 94.418 94.473 94.528 94.582 94.636 94.689 94.741 94.793 94.845 94.896 94.947 94.997 95.046 95.095 95.144 95.192 95.239 95.287 95.333 95.379 95.425 95.470 95.515 95.560 95.604 95.647 95.690 95.733 95.775 95.817 95.858 95.899 95.940 49.585 49.593 49.601 49.609 49.617 49.624 49.632 49.639 49.646 49.653 49.660 49.666 49.673 49.679 49.686 49.692 49.698 49.704 49.710 49.715 49.721 49.726 49.732 49.737 49.742 49.747 49.752 49.757 49.762 49.766 49.771 49.776 49.780 49.784 49.788 49.793 49.797 49.801 49.805 49.808 49.812 49.816 49.819 49.823 49.826 49.830 49.833 49.836 49.840 49.843 49.846 49.849 49.852 49.855 49.858 49.860 49.863 49.866 49.869 49.871 49.874 49.876 49.879 49.881 49.883 49.886 49.888 49.890 49.892 49.894 49.896 49.898 49.900 49.902 49.904 49.906 49.908 49.910 49.912 49.913 49.915 33.307 33.308 33.309 33.309 33.310 33.311 33.311 33.312 33.313 33.313 33.314 33.314 33.315 33.316 33.316 33.317 33.317 33.318 33.318 33.318 33.319 33.319 33.320 33.320 33.321 33.321 33.321 33.322 33.322 33.322 33.323 33.323 33.323 33.324 33.324 33.324 33.324 33.325 33.325 33.325 33.325 33.326 33.326 33.326 33.326 33.326 33.327 33.327 33.327 33.327 33.327 33.328 33.328 33.328 33.328 33.328 33.328 33.328 33.329 33.329 33.329 33.329 33.329 33.329 33.329 33.330 33.330 33.330 33.330 33.330 33.330 33.330 33.330 33.330 33.330 33.330 33.331 33.331 33.331 33.331 33.331 24.998 24.998 24.998 24.998 24.998 24.998 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 24.999 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 9.091 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 8.333 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.692 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 7.143 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 6.667 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 95.980 96.020 96.059 96.098 96.137 96.175 96.213 96.251 96.288 96.325 96.361 96.397 96.433 96.468 96.503 96.538 96.572 96.606 96.639 96.673 96.706 96.738 96.771 96.803 96.834 96.866 96.897 96.927 96.958 96.988 97.018 97.047 97.076 97.105 97.134 97.162 97.191 97.218 97.246 97.273 97.300 97.327 97.353 97.380 97.405 97.431 97.457 97.482 97.507 97.531 97.556 97.580 97.604 97.628 97.651 97.674 97.698 97.720 97.743 97.765 97.787 97.809 97.831 97.852 97.874 97.895 97.916 97.936 97.957 97.977 97.997 98.017 98.036 98.056 98.075 98.094 98.113 98.132 98.150 98.168 98.187 49.917 49.918 49.920 49.921 49.923 49.924 49.926 49.927 49.929 49.930 49.932 49.933 49.934 49.936 49.937 49.938 49.939 49.940 49.942 49.943 49.944 49.945 49.946 49.947 49.948 49.949 49.950 49.951 49.952 49.953 49.954 49.955 49.956 49.957 49.957 49.958 49.959 49.960 49.961 49.961 49.962 49.963 49.964 49.964 49.965 49.966 49.966 49.967 49.968 49.968 49.969 49.970 49.970 49.971 49.971 49.972 49.972 49.973 49.974 49.974 49.975 49.975 49.976 49.976 49.977 49.977 49.977 49.978 49.978 49.979 49.979 49.980 49.980 49.980 49.981 49.981 49.981 49.982 49.982 49.983 49.983 33.331 33.331 33.331 33.331 33.331 33.331 33.331 33.331 33.331 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.332 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 33.333 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 16.667 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 14.286 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 12.500 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 11.111 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 9.091 9.091 9.091 9.091 9.091 9.091 9.0
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started