An investment will pay $50 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6.

If other investments of equal risk earn 11% annually, what is its present value? Round your answer to the nearest cent. $686.79

If other investments of equal risk earn 11% annually, what is its future value? Round your answer to the nearest cent. $____

1. If you deposit $9,000 in a bank account that pays 12% interest annually, how much would be in your account after 5 years? Round your answer to the nearest cent. a. $15,861.08 What is the present value of a security that will pay $26,000 in 20 years if securities of equal risk pay 3% annually? Round your answer to the nearest cent. $22,427.83 Your parents will retire in 24 years. They currently have $300,000, and they think they will need $1,350,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places. N=6.47 If you deposit money today in an account that pays 7% annual interest, how long will it take to double your money? Round your answer to two decimal places. 10.24 years You have $46,808.11 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $290,000. You expect to earn 14% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations. N= 20.32 Future value: annuity versus annuity due a What's the future value of a 9%, 5-year ordinary annuity that pays $400 each year? Round your answer to the nearest cent. 2,393.88 b If this was an annuity due, what would its future value be? Round your answer to the nearest cent. 2,609.33 An investment will pay $50 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. b c If other investments of equal risk earn 11% annually, what is its present value? Round your answer to the nearest cent. 686.79 If other investments of equal risk earn 11% annually, what is its future value? Round your answer to the nearest cent. You want to buy a car, and a local bank will lend you $30,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 11% with interest paid monthly. What will be the monthly loan payment? Round your answer to the nearest cent. What will be the loan's EAR? Round your answer to two decimal places. Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Round your answers to the nearest cent. d An initial $300 compounded for 1 year at 10%. e An initial $300 compounded for 2 years at 10%. f The present value of $300 due in 1 year at a discount rate of g The present value of $300 due in 2 years at a discount rate of 10%. Find the following values. Compounding/discounting occurs annually. Round your answers to the nearest cent. h An initial $700 compounded for 10 years at 6%.$ i An initial $700 compounded for 10 years at 12%. $ j The present value of $700 due in 10 year at a discount rate of 6%.$ k The present value of $2,770 due in 10 years at 12%.$ l The present value of $2,770 due in 10 years at 6%.$ m 1 2 3 4 5 Define present value. The present value is the value today of a sum of money to be received in the future and in general is less than the future value. The present value is the value today of a sum of money to be received in the future and in general is greater than the future value. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value. The present value is the value in the future of a sum of money to be received today and in general is less than the future value. The present value is the value in the future of a sum of money to be received today and in general is greater than the future value. n How are present values affected by interest rates Shalit Corporation's 2011 sales were $14 million. Its 2006 sales were $7 million. o At what rate have sales been growing? Round your answer to two decimal places. Suppose someone made this statement: "Sales doubled in 5 years. This represents a growth of 100% in 5 years, so, dividing 100% by 5, we find the growth rate to be 20% per year." Is that statement correct? Find the interest rates earned on each of the following. Round each answer to two decimal places. p You borrow $750 and promise to pay back $780 at the end of 1 year. q You lend $750 and the borrower promises to pay you $780 at the end of 1 year. r You borrow $79,000 and promise to pay back $139,225 at the end of 5 years. You borrow $15,000 and promise to make payments of $4,058.60 at the end of each year for 5 years. How long will it take $700 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places. s 7%.____(years) t 11%. ____(years) u 19%.____(years) v 100%.____(years) Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent. w$1,000 per year for 4 years at 12%.$ x $500 per year for 2 years at 6%. $ y $400 per year for 16 years at 0%.$ z Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent. aa $1,000 per year for 4 years at 12%.$ ab ac $500 per year for 2 years at 6%. $ $400 per year for 16 years at 0%.$ Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent. ad $300 per year for 12 years at 4%.$ ae $150 per year for 6 years at 2%. $ af $700 per year for 6 years at 0%.$ Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent. ag $300 per year for 12 years at 4%.$ ah $150 per year for 6 years at 2%. $ ai $700 per year for 6 years at 0% Present value of a perpetuity ajWhat is the present value of a $500 perpetuity if the interest rate is 8%? Round your answer to the nearest cent. $ If interest rates doubled to 16%, what would its present value be? Round your answer to the nearest cent. Effective interest rate You borrow $155,000; the annual loan payments are $8,963.67 for 30 years. What interest rate are you being charged? Round your answer to two decimal places. Uneven cash flow stream Find the present values of the following cash flow streams at 12% compounded annually. Round your answers to the nearest cent. Stream A $ Stream B $ What are the PVs of the streams at 0%, compounded annually? Stream A $ Stream B $ Future value of an annuity Your client is 37 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $4,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future. If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.$ How much will she have at 70? Round your answer to the nearest cent.$ She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Round your answers to the nearest cent. Annual withdrawals if she retires at 65 $ Annual withdrawals if she retires at 70 $ Evaluating lump sums and annuities Crissie just won the lottery, and she must choose between three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.3 million, or 30 end-of-year payments of $5.4 million. ak If she thinks she can earn 7% percent annually, which should she choose? 1 Select 1She should accept the 30year payment option as it carries the highest present value She should accept the lumpsum payment option as it carries the highest present value She should accept the 10year payment option as it carries the highest present value She should accept the lumpsum payment option as it carries the highest future value 2 3 4 5 alIf she expects to earn 8% annually, which is the best choice? 1 Select 1She should accept the lumpsum payment option as it carries the highest present value She should accept the 30year payment option as it carries the highest present value She should accept the 10year payment option as it carries the highest present value She should accept the lumpsum payment option as it carries the highest future value am 2 3 4 5 If she expects to earn 9% annually, which would you recommend?SelectShe should accept the lumpsum payment option as it produces the highest present valueShe should accept the 30year payment option as it produces the highest present value.She should accept the 10year payment option as it produces the highest present valueShe should accept the 30year payment option as it produces the highest future value Explain how interest rates influence the optimal choice. SelectThe higher the interest rate, the more valuable it is to get money rapidly The lower the interest rate, the more valuable it is to get money rapidly The higher the discount rate, the higher the more distant cash flows are valued Interest rates do not influence the optimal choice in any way Interest rates and the present value of cash flows are positively related Loan amortization Jan sold her house on December 31 and took a $50,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. an What is the dollar amount of each payment Jan receives? Round your answer to the nearest cent.$ ao ap How much interest was included in the first payment? Round your answer to the nearest cent. $ How much repayment of principal was included? Round your answer to the nearest cent. aq $ How do these values change for the second payment? SelectI II III IV V 1 2 3 4 I. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases. II. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal decreases. III. The portion of the payment that is applied to interest and the portion of the payment that is applied to principal remains the same throughout the life of the loan. IV. The portion of the payment that is applied to interest 5 declines, while the portion of the payment that is applied to principal also declines. V. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal also increases. How much interest must Jan report on Schedule B for the first year? Round your answer to the nearest cent.$ Will her interest income be the same next year? SelectHer interest income will increase in each successive year Her interest income will remain the same in each successive year She will not receive interest income, only a return of capital Her interest income will decline in each successive year She will receive interest only when the mortgage is paid off in 10 years If the payments are constant, why does the amount of interest income change over time? SelectI II III IV V 6 7 8 I. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal increases. II. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases. III. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal declines. IV. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal declines. V. As the loan is amortized (paid off), the beginning balance declines, but the interest charge and the repayment of principal remain the same. Future value for various compounding periods Find the amount to which $500 will grow under each of these conditions: 12% compounded annually for 5 years. Round your answer to the nearest cent.$ 12% compounded semiannually for 5 years. Round your answer to the nearest cent.$ 12% compounded quarterly for 5 years. Round your answer to the nearest cent.$ 12% compounded monthly for 5 years. Round your answer to the nearest cent.$ 12% compounded daily for 5 years. Round your answer to the nearest cent.$ Why does the observed pattern of FVs occur? SelectThe future values increase because as compounding periods per year increase, interest is earned on interest less frequently The future values decrease because as compounding periods per year increase, interest is earned on interest more frequently The future values increase because as compounding periods per year increase, interest is earned on interest more frequently The future values increase because as compounding periods per year decrease, interest is earned on interest more frequently The future values decrease because as compounding periods per year decrease, interest is earned on interest more frequently Present value for various discounting periods Find the present value of $600 due in the future under each of these conditions: 7% nominal rate, semiannual compounding, discounted back 5 years. Round your answer to the nearest cent. $ 7% nominal rate, quarterly compounding, discounted back 5 years. Round your answer to the nearest cent. $ 7% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent. $ Why do the differences in the PVs occur? SelectThe present values decline as the discounting periods per year increase The present values decline as the discounting periods per year decrease The present values increase as the discounting periods per year increase The present values are not affected by changes in the number of discounting periods per year The present values are positively related to the number of discounting periods per year Find the present value of $600 due in the future under each of these conditions: 7% nominal rate, semiannual compounding, discounted back 5 years. Round your answer to the nearest cent. $ 7% nominal rate, quarterly compounding, discounted back 5 years. Round your answer to the nearest cent. $ 7% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent. $ Why do the differences in the PVs occur? SelectThe present values decline as the discounting periods per year increase The present values decline as the discounting periods per year decrease The present values increase as the discounting periods per year increase The present values are not affected by changes in the number of discounting periods per year The present values are positively related to the number of discounting periods per year Future value of an annuity Find the future values of the following ordinary annuities: FV of $600 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. Round your answer to the nearest cent. $ FV of $300 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly. Round your answer to the nearest cent. $ These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in Part b ends up larger than the one in Part a. Why does this occur?Select The nominal deposits into the annuity in part (b) are greater than the nominal deposits into the annuity in part (a). The annuity in part (a) is compounded less frequently; therefore, more interest is earned on interest.The annuity in part (a) is compounded more frequently; therefore, more interest is earned on interest. The annuity in part (b) is compounded less frequently; therefore, more interest is earned on interest. The annuity in part (b) is compounded more frequently; therefore, more interest is earned on interest. You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $400. The loan will have a 11% APR based on end-of-month payments. What is the most expensive car you could afford if you finance it for 48 months? Round your answer to the nearest cent. $ What is the most expensive car you could afford if you finance it for 60 months? Round your answer to the nearest cent.$ Effective versus nominal interest rates Bank A pays 9.5% interest compounded annually on deposits, while Bank B pays 9% compounded daily. Based on the EAR (or EFF%), which bank should you use? SelectI II III IV V 9 10 11 12 13 I. You would choose Bank A because its EAR is higher. II. You would choose Bank B because its EAR is higher. III. You would choose Bank A because its nominal interest rate is higher. IV. You would choose Bank B because its nominal interest rate is higher. V. You are indifferent between the banks and your decision will be based upon which one offers you a gift for opening an account. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest. 14 I.If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable. 15 II. If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you have no intentions of making a withdrawal during the year, then Bank B might be preferable. 16 III. If funds must be left on deposit until the end of the compounding period (1 day for Bank A and 1 year for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable. 17 IV. If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable. 18 V. If funds must be left on deposit until the end of the compounding period (1 day for Bank A and 1 year for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable. Amortization schedule Set up an amortization schedule for a $48,000 loan to be repaid in equal installments at the end of each of the next 3 years. The interest rate is 10% compounded annually. Round all answers to the nearest cent. What percentage of the payment represents interest and what percentage represents principal for each of the 3 years? Round all answers to two decimal places. Why do these percentages change over time? 19 These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the balance declines. 20 These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the balance declines. 21 These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the balance increases. 22 These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the balance increases. These percentages do not change over time; interest and principal are each a constant percentage of the total payment. Paying off credit cards Simon recently received a credit card with an 14% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $350. The minimum payment on the card is only $10 per month. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Round your answer to the nearest whole. ___ month(s) If Simon makes monthly payments of $30, how many months will it be before he pays off the debt? Round your answer to the nearest whole. ____ month(s) How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan. Make sure you use 3 decimal places for N. Round your answer to the nearest cent.$ Required lump sum payment Starting next year, you will need $20,000 annually for 4 years to complete your education. (One year from today you will withdraw the first $20,000.) Your uncle deposits an amount today in a bank paying 6% annual interest, which will provide the needed $20,000 payments. How large must the deposit be? Round your answer to the nearest cent.$ How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent