LEARNING COMPETENCIES After studying this module, you will be able to do the following: Find the amount of simple and compound interest; Ascertain exact, ordinary interest, maturity value, and simple discount; Obtain principal, rate and time; OUTLINE 1. II. III. IV. Simple Interest. Finding the Principal, Rate and Time. Simple Discount Compound Interest BASIC CONCEPTS Some individuals or entities borrow or lend money to secure funds for their own purposes. The individual or entity which borrow money is the debtor or lendee, while the one which lends money is the creditor or lender. Interest refers to the fee or payment for the use of money. Interest rates are usually expressed as a percent of the amount borrowed, lent, deposited or invested. For instance, an entity may charge 10% per year on money borrowed for a car or a housing loan or for an individual for items obtained through credit card. There are two types of interests: Simple Interest and Compound Interest. The Simple Interest is the interest charged on the principal alone for the entire length of the loan. Simple interest loans are usually offered by banks to individuals and businessmen for short-term periods. The simple interest is paid back either at the end of the period or deducted in advance in one year or less. The compound interest is the interest on the principal and the interests earned on previous periods. This means that a sum of money invested for one year that earns interest compounded quarterly will earn simple interest for the first quarter. The interest earned is added to the original principal to have a new principal. This new principal now becomes the basis for calculating the interest for the second quarter, and the process is repeated until the fourth quarter. 1 - SIMPLE INTEREST Simple interest is usually used for short borrowings such as those obtained for less than one (1) year. There are however, transactions where periods involve more than a year. The amount of simple interest is determined using three factors: the Principal or debt, the rate of interest, and the duration or length of time. The Principal refers to the amount borrowed, deposited or invested or P. The rate of interest refers to the Percentage of the principal per year generally expressed in terms of percent (%) per year denoted as R. The time, represented by T, refers to the length of time or period from the date of loan is made to the date the loan becomes due or payable. The time is calculated usually on a per year basis. A simple interest, denoted by I, is interest charged on the principal; for the entire duration or period of the loan. It is determined using the following formula: Simple Interest (1) = Principal P x Rate Rx Time Tor I = PRT The rate of interest, expressed in percent (%), must first be converted to a decimal number, and the time must also be converted into a year before it is substituted to the formula. Example: 5 /A % rate of interest has be changed first to 0.0525, or a time of 5 months has to be expressed first to 5/12 of a year or period of 23 months to 23/12 Finding the Amount of Simple Interest A. Finding the Simple Interest if Time is in Years: 1. Use I = PxRxT or I = PRT 2. Express the rate in decimal form and the time in years. 3. Substitute the values in the formula and solve for the interest. Examples: 1. A man borrowed P25,000.00 for 2 /years at 8% per year. Find the amount of simple interest. Given: P = P25,000.00 R = 8% or 0.08 T = 2 years Solution: Change 8% to 0.08 and 2 4 years to 2.25 years. Substitute the values to the formula. 1 = PRT = P25,000.00 x 0.08 x 2.25 = P4,500.00 2. Find the amount of simple interest on a loan of P13,400.00 for 1 % years at 8 %% per year. Given: P = P13,400.00 R = 8 %% or 0.0875 T = 1% years Solution: Express 87% to 0.0875 and 14 years to 5/3 years. Substitute the values to the formula. I = PRT = P13,400.00 x 0.0875 x 5/3 | = P1,954.17 (rounded to the nearest centavo) 3. Mr Reyes obtained s loan of P45,000.00 from a credit union that charges 8.5% simple interest for 3 %2 years. Determine the: a. amount of interest per annum b total amount of interest due on the loan Given: P= P45,000.00 R = 8.5% or 0.085 T=3%2 years Solution: a. Express 8.5% to 0.085 and use 1 year for time per annum. Substitute the values in the formula. I = PRT = P45,000.00 x 0.085 x 1 = P3,825.00 b. Convert 8.5% to 0.085 and convert 3 12 years to 3.5 years. Substitute the values in the formula. I = PRT = P45,000.00 x 0.085 x 3.5 = P13, 387.50 Finding the Simple Interest if Time is in Months To obtain the simple interest if the time is expressed in moths, observe the following procedures: 1. Use I =PRT 2. Express the rate in decimal form and the time in years by diving the number of months by 12 months. 3. Substitute the values in the formula and solve the simple interest. Examples: 1. How much is the simple interest on P17,600.00 for 7 months at 7.5%? Given: P=17,600.00 R = 7.5% or 0.075 T = 7 months or 7/12 years Solution: Express 7.5% to 0.075 and divide 7 months by 12 months to obtain 7/12 years. Then, Substitute the values in the formula. I = PRT = P17,600.00 x 0.075 x 7/12 = P770.00 2. A loan of P28,900.00 is obtained for 5 months at 8 3/5%. How much is the Simple Interest? Given: P = 28,900.00 R = 8 3/5% or 0.086 T = 5 months or 5/12 years Solution: Express 8 3/5% to 0.086 and 5 months to 5/12, then, substitute the values in the formula. I = PRT = P28,900.00 x 0.086 x 5/12 = P1,035.38 (rounded to the nearest centavo) 3. A man obtained a loan of P54,000.00 for 2 years and 11 months at 8.35%. How much was the simple interest? Given: P = 54,000.00 R = 8.35% or 0.0835 T = 2 11/12 years Solution: Express 8.35% to 0.0835 and 2 years and 11 months to 2 11/12 then to 35/12 years and substitute to the formula. I = PRT = P54,000.00 x 0.0835 x 2 11/12 = P54,000.00 x 0.0835 x 35/12 I = P13,151.25 Finding the Number of Days from One Date to Another While the periods of many loans are expressed in months, it is a common practice for loans to be payable after a certain number of days such as 30 days or 145 days. The duration of the loan may even be for a particular period such as July 10 to November 11 of the same year. There are two methods to find the number of days from one date to another: 1) Method A involves manual counting of the actual number of days from a specific beginning date to a specific ending date of the month and the actual number of days in each month. In doing this, do not count the day of the transaction but count the day when the transaction is completed or disregard the first day but count the last day. 2) Method B involves using a Table (which could be found in the internet) where the days corresponding to the beginning and ending dates are indicated. To find the number of days from date to another following Method B, follow the steps below: a. Find the days corresponding to the beginning and ending dates using the Table. b. Find the difference between the number of days corresponding to the ending date and the beginning date id the dates belong to the same year. c. If the dates belong to 2 successive years, subtract from 365 days the number of days corresponding to the beginning date and add the result to the number of days corresponding to the ending date. Note that in both methods, add 1 day (February 29) to the resulting number of days if the period covers a leap year. Examples: 1. Find the number of days from March 25 to July 15 of the same year by: a. manual counting based on calendar months b. using table Solutions: a. By manual counting using the actual number of days in each month: disregard 1st count last March 25 - 31 6 days April 1 - 30 30 days May 1 - 31 31 days June 1 - 30 30 days July 1 - 15 15 days 112 days Hence, there are 112 days from March 25 to July 15 of same year b. Using Table, we shall have the following: July 15 is 196 days from January 1 March 25 is 84 days from January 1 Hence, 196 days - 84 days = 112 days 2. Using the Table, determine the number of days between the following dates: a. October 5 to February 7 of the following year. b. January 25 to December 12 of the same year (not leap year) c. August 15 to March 18 of the following year (a leap year) Solution: a. October 5 is day 278. Hence 365 278 = 87 days from October 5 to December 31 of same year. Thus we shall have: October 5 to December 31fo same year = 87 days January 1 to February 7 of next year = 38 days 125 days from October 5 to February 7 of the following year. b. January 1 to December 12 = 346 days January 1 to January 25 = 25 days 321 days from January 25 to December 12 (not a leap year) c. January 1 to December 31 = 365 days January 1 to August 15 = 227 days 138 days from August 15 to December 31 January 1 to March 18 = 78 days 216 days + 1 (a leap year) from August 15 to March 18 the following year There are two ways to remember the number of days in a month: the Knuckle Method and the Rhyme Method. THE KNUCKLE METHOD Jul & Aug (31 days) Jun & Sep (30 days) May & Oct (31 days) Apr & Nov (30 days) Mar & Dec (31 days) Feb (28 days) Jan (31 days) The Rhyme Method "Thirty days has September, April, June and November. All the rest have thirty-one, Except February has twenty-eight. Leap year comes one year in four, and gives to February one day more." Exact and Ordinary Interest As discussed earlier, simple interest rates are based on the annual rate such as 6% or 8 14% per year. The time must be expressed in years or fraction of a year. If the time is given in number of days, it shall be converted to a fraction of a year, by dividing it by the number of days in a year. Exact interest is used when computations require the use of the exact number of days in a year, 365 days or 366 days (1 day is added after the end of February in a leap year). We shall use the symbol le for exact interest. le = PRT T = Exact Number of Days 365 (or 366 days if a leap year) Ordinary interest or banker's interest is used when interest is computed on the basis of an assumed 30-day period per month or 360 days in one year. lo shall be used to denote ordinary interest. The formula for ordinary or banker's interest is: lo = PRT Exact Number of Days T = 360 days Examples: 1. An amount of P37,500.00 was borrowed at 8 % % simple interest for 120 days. Compute the a) exact interest; b) ordinary interest. Given: P = 37,500.00 R = 81% or 0.085 T = 120 days Solution: a. Exact Interest: le = PRT 120 = P37,500.00 x 0.085 x 365 le = P1,047.95 (rounded to the nearest centavo) b. Ordinary Interest: lo = PRT 120 = P37,500.00 x 0.085 x 360 lo = P1,062.50 2. An amount of P54,000.00 is invested at 8% simple interest on March 15. Find the amount of a) exact interest, and b) ordinary interest earnings by August 11 of the same year and determine the c) difference in earnings between the ordinary (banker's) interest and exact interest. Given: P = P54,000.00 R = 8% or 0.08 T - March 15 to August 11 of the same year Solutions: a. Exact Interest The exact number of days is: August 11 = day 223 March 15 = day 74 149 days, Hence, le = PRT 149 = P54,000.00 x 0.08 x 365 le = P1,763.51 (rounded to the nearest centavo) b. Ordinary or banker's interest lo = PRT 149 = P54,000.00 x 0.08 x 360 lo = P1,788.00 c. The difference between the interest earnings under ordinary (banker's) interest and exact interest is P24.49 calculated as follows: Difference = Ordinary (banker's) interest - exact interest = P1,788.00 - P1,763.51 = P24.49 Maturity Value When a certain amount of money is deposited or borrowed, the sum of money at the end of the period is called maturity or accumulated value. The maturity or accumulated value is, therefore, equal to the sum of the principal or face value and the interest earned. If we let the symbol M be the maturity or accumulated value, then, we have: Maturity Value (M) = Principal (P) + Interest (1) Or M = P + 1 Since I = PRT, then we have: M= P + PRT And M=P (1 +RT) Finding the Maturity Value To determine the maturity value of a loan, observe the following procedures: Method A: 1. Use I = PRT to find I. 2. Find M using M = P + Method B: 1. Use the formula M = P(1 +RT) 2. Substitute the value in the formula and solve the maturity value. Examples: 1. Find the maturity value of a loan of P18,000.00 made for 2 years at 8% simple Interest Given: P = P18,000.00 R = 8% or 0.08 T = 2 years Solutions: Method A: 1 = PRT = P18,000.00 x 0.08 x 2 I = P2,880.00 Then, M = P + 1 = P18,000.00 + P2,880.00 M = P20,880.00 Method B: M = P (1 +RT) = P18,000.00 (1 + (0.08 x 2)] = P18,000.00 [1 + 0.16] = P18,000.00 [1.16] M = P20,800.00 2. A sum of P43,200.00 is borrowed for 11 months at 7 1/5% simple interest. Determine the maturity value of the loan. Given: P = P43,200.00 R = 7 1/5% or 0.072 T = 11 months Solutions: Method A: I = PRT = P43,200.00 x 0.072 x 11/12 = P2,851.20 Then, M= P + 1 = P43,200.00 + P2,851.20 M= P46,051.20 Method B: M = P(1 +RT) = P43,200.00 (1 + (0.072 x 11/12)] = P43,200.00 [1 + (0.066)] = P43,200.00 (1.0066] M = P46,051.20 3. Miss Mahusay borrowed P25,800.00 from a credit union that charges 82% simple interest. If she will pay the loan at the end of 3/2 years, how much would she have to pay by then? Solve using the two methods. Given: P = P25,800.00 R = 8 %%% or 0.0875 T = 3 2 years Solutions: Method A: I = PRT = P25,800.00 x 0.0875 x 3.5 years = P7,901.25 Then M = P + = P25,800.00 + P7,901.25 = P33,701.25 Method B: M = P(1+RT) = 25,800.00 [1 + (0.0875 x 3.5)] M = P33,701.25 II - FINDING THE PRINCIPAL, RATE and TIME Finding the Principal In our discussion on simple interest, we calculated the interest given the principal, rate and time. Now, we will solve the either the principal, rate or time given the interest and two (2) of these items. The principal (P) refers to the sum of money invested, deposited or borrowed. It is found by dividing both sides of the equation for simple interest, I = PRT, by RT. Thus, we have: Interest (1) Principal (P) = Rate (R)x Time (T) in years RT The principal is also known as the present value. There is, however, a slight difference between the principal and the present value. The present value of a certain amount is how much that money is worth today. But, if the amount of money is not used or paid back for years, then that money will not probably be worth as much as at some future time because of inflation. For example, a kilo of an item worth P180.00 today may not be worth as much three (3) years later. Hence, we will use the term principal instead of present value throughout our discussion in this topic. Examples: 1. A vendor borrows a certain amount of money at 8% simple interest for 3 months. Determine the principal that results in interest amounting to P600.00. Given: I = P600.00 R= 8% or 0.08 T = 3 months Solutions: 1 P= RT P600.00 3 0.08x 12 = P30,000.00 2. Mr. Pogi was charged P1,900.00 on a loan for 144 days at 9 % % simple interest Determine the amount of the a. original loan b. amount he paid at the end of 144 days Given: P= P1,900.00 R=95% or 0.095 T = 144 days Solutions: a. For the original loan: I P= RT 1,900.00 144 0.095x 360 1,900.00 .095x144 360 1,900.00 13.68 360 1,900.00 0.038 = P50,000.00 b. For the amount he paid at the end of 144 days: M= P + = P50,000.00 + P1,900.00 = P51,900.00 Finding the Rate The Rate (R) refers to the to the percentage of the principal per year. It is generally expressed in terms of percent (%). To find the rate, solve for R in the formula I = PRT by dividing both sides of the equation by PT. Hence, Rate of Interest (R) Interest (1) Principal (P)x Time (T) in years x 100% 1 R= x 100% PT Examples: 1. A man deposits P90,000.00 in a savings bank for 5 months. If the interest amounts to P1,875.00, find the rate of interest. Given: P = P90,000.00 | = P1,875.00 T = 5 months Solution: R = x 100% PT P1,875.00 -x100% P90,000.00x 12 P1,875.00 -x100% P37,500.00 R = 5% 2. If P60,000.00 was deposited in a bank and became P61,625.00 at the end of 150 days, find the interest rate. Given: P = 60,000.00 M = P61,625.00 T = - 150 days Solutions: Since M = P61,625.00 and P-60,000.00, then, | = M-P = P61,625.00 P60,000.00 1 = P1,625.00 Hence, we have: R= 1 -x100% PT P1,625.00 X100% 150 P60,000.00x 360 P1, 625.00 -X100% P25,000.00 R=6.5% Finding Time The time (T) refers to the length of time from the date the transaction is made to the maturity date. The time is usually expressed in years, unless otherwise specified such as in number of months or in days. The time is calculated by dividing both sides of the equation for simple interest, I = PRT by PR. Thus, we have: Time (T in years Interest(I) Principal(P)xRate(R) PR If we will express the time in years to time in moths or days, we shall observe the following steps and procedures: To convert the time in years to: a. time in months, use the formula: Timelinmonths) 1 -x12 PR x360 b. time in days, use the formula: Examples: Time (in days) PRE 1. Ryker John deposited P80,000.00 in a savings account that pays 4 %% simple interest and earned P10,800.00 in interest. How long in years did it takes Ryker John to ear the interest? Given: P = P80,000.00 | = P10,800.00 R = 4% or 0.045 Solution: Substitute the values in the formula, as follows: 1 Time(inyears) PT P10,800.00 P80,000.00x0.045 P10,800.00 P3,600.00 Time (in years) = 3 years 2. How many days did it take Romy to place P120,000.00 in an investment house that pays 8% simple interest before he obtained an interest of P4,000.00? Given: P = P120,000.00 | = P4,000.00 R = 8% or 0.08 Solution: Substituting the given values in the formula, we shall have: 1 Timelindays) -x360 PR P4,000.00 -x360 P120,000.00x0.80 4,000.00 -x360 9,600.00 Time (in days) = 150 days III - SIMPLE DISCOUNT In simple interest, the principal or face value is the amount or the proceeds actually received by the borrower from the lender. Therefore, the borrower pays back at maturity date the principal plus the amount of interest earned on the principal (M = P + 1). In simple discount, however, the interest is deducted in advance from the principal or face value of the note. The borrower, therefore, does not receive the principal or face value of the note but rather the proceeds. The proceeds is the difference between the value and the interest for the period. The face value in this case becomes the maturity value which the borrower shall pay at maturity date. This maturity value is, thus, the sum of the proceeds and the interest. The interest here which is deducted in advance is called bank discount or simply discount. Hence, in simple discount, we use the following formulas to find the bank discount, proceeds, and face value or maturity value: Bank Discount (B) = Maturity Value (M) x Discount Rate (D) x Time (T) in years or B = MDT Proceeds (Pr) = Maturity Value (M) - Bank Discount (B) or Pr = M-B Maturity Value (M) = Proceeds (Pr) + Bank Discount (B) or M = Pr +B From the formula B = MDT, we can derive the following formulas: Bank Discount (B) Maturity Value (M) = Discount Rate (Dx Time (T)in years B or M= DT Bank Discount (B) Discount Rate (D) = x 100% Maturity Value (M)x Time (T)in years B or D = 100% MT Bank Discount (B) Time (T) in Years = Maturity Value (M)x Discount Rate (D) B or T= MD Please note, however, that while the formula for bank discount is similar to the simple interest formula, we shall have different symbols or letters to have distinctions between ideas. Please remember that a simple interest is computed based on the principal while simple discount is computed on the maturity value or face value. Examples: 1. Find the a) interest that will be deducted in advance and the b) proceeds from a loan of P25,000.00 due in two years if the discount rate is 6%. Given: M = P25,000.00 D = 6% or 0.06 T = 2 years Solutions: The amount of loan of P25,000.00 is interpreted here as the maturity value or the face value. Hence, we have: a) the interest deducted in advance B = MDT = P25,000.00 x 0.6 x 2 B = 3,000.00 b) the proceeds from the loan Pr=M-B = P25,000.00 - P3,000.00 Pr = P22,000.00 2. Mr. T. Cocoan borrowed P20,000.00 from a credit entity that is due in 250 days. If he was charged P1,600.00 interest deducted in advance, find the discount rate. Given: M = P20,000.00 B = P1,600.00 T = 250 days Solution: Substituting the given values in the formula, we obtain: B D=>X 100% MT P1,600.00 250 -*100% P20,000.00x 360 P1,600.00 x100% 13.888.89 = 11.52% 3. Ral Sean borrowed a certain amount of money from a lending institution and was charged P3,000.00 simple discount. If the discount rate is 10% for a 9-month period, how much: a. was the amount of his loan? b. proceeds did he obtain? Given: B = P3,000.00 D = 10% or 0.10 T = 9 months Solutions: a. For the amount of loan: B M= DT P3,000.00 0.10x2 12 P3,000.00 0.075 M = P40,000.00 b. The proceeds is calculated as follows: Pr = M-B = P40,000.00 - P3,000.00 Pr = P37,000.00 4. Ral Natan borrows a sum of money from a credit union for 135 days. If an 8% discount rate is charged, find the maturity value of the simple discount note that results in proceeds of P50,000.00 for him. Given: Pr = P50,000.00 D = 8% or 0.08 T = 135 days Solutions: From the formula for proceeds, we derive M as follows: Pr = M-B But B = MDT So, Pr = M - MDT By Factoring Pr = M(1-DT) Therefore, Axiom of Division 1-DT Substituting the values in the formula, we have: M Pr M= Pr 1-DT P50,000.00 135 1-[0.08x 360 P50,000.00 1-(0.03) P50,000.00 0.97 M = PS 1,546.39 5. A simple discount note has a face value of P28,000.00 and proceeds of P27,000.00. Find the discount rate if the note is for 125 days. Given: M = P28,000.00 Pr = P27,000.00 T= 125 days Solutions: Find the discount as follows: B = M-Pr = P28,000.00 - P27,000.00 B = P1,000.00 B DEX 100% MT 1,000.00 -x100% 125 28,000.00x 360 = 10.29% (rounded to hundredths place) IV-COMPOUND INTEREST As earlier stated, the compound interest is the interest on the principal and the interests of the previous periods. Compound interest is usually used by banks in calculating interest for long-term investments and loan such as savings account and time deposits. Interest may be compounded periodically such as annually, semi-annually, quarterly, monthly or daily over the life of the investment or loan. The Compound Amount and Interest The compound amount or future value is the final amount of the investment or loan at the end of the term or last period. The compound interest is the difference between compound amount and the original capital. In calculating compound interest, the formulas for simple interest, I = PRT and M = P + 1, are used each period compound interest is computed. For example, if P10,000.00 is invested for 3 years at 8% compounded annually, the compound amount and the interest shall be calculated as follows: Given: P = P10,000.00 R = 8% or 0.08 T = 3 years First Year Second Year Third Year Solution: Using I = PRT and M = P + I, we have: Interest New Principal P10,000.00 x 0.08 x 1 = P800.00= P10,800.00 P10,800.00 x 0.08 x 1 P864.00 = P11,664.00 P11,664.00 x 0.08 x 1 P933.12 = P12,597.12 Total P2,597.12 Therefore, at the end of 3 years, the compound amount is P12,597.12 and the compound interest is P2,597.12. Before calculating compound amount and interest, it is better to familiarize first with the following terms: A. Interest Compounded Number of interest/compounding Periods in 1 year 1. Annually or once a year 1 2. Semi-annually or every 6 months 2 3. Quarterly or every 3 months 4 4. Monthly or once a month 12 5. Daily or once a day 365/366 (leap year) B. Terms 1. Conversion Period or interest period. This is the time between two successive conversions of interest. 2. Frequency of Conversion. This is the number of conversion periods of the investment or loan per year. It is denoted by m. Examples: monthly (m = 12) and quarterly (m = 4) 3. Nominal Rate. This is the stated rate of interest per year, denoted by j. Example: j = 8% means 8% interest per year. 4. Rate per Conversion Period. This is the rate of interest for each conversion period, denoted by i. Therefore, Nominal Rate Frequency of Conversion 1 m Examples: For 8% compounded quarterly, i = i 8% = 2% = 0.02 4 m 9% For 9% compounded monthly, i %% or 0.75% or 0.0075 m 12 5. Number of Conversion Periods. This is the total number of times interest is calculated for the entire term if the investment or loan. It is denoted by n and obtained by multiplying the time in years by the frequency of conversion per year. Thus, n = time in years x frequency conversion or n=txm Examples: If t = 2 years compounded quarterly, then n=txm or n=2 years x 4 periods per year = 8 Ift = 2 years and 5 months compounded monthly, then 5 n = 2 years x 12 periods per year = 29 12 If t = 3 years and 9 months compounded every 3 months, then na: 312 years x 4 periods per year = 15 Finding the Compound Amount and Interest The compound amount (M) and compound interest (1) can be calculated by using the following formulas: M = P(1 + )" or M = P(1 + i)" and I = M-P where P = Original principal M = compound amount or maturity value or accumulated value of P at the end of n periods. j = nominal rate or annual rate of interest m = frequency (t) of conversion per year i = interest rate per conversion period t = term of investment or loan in years n = total number of conversion periods in the investment term Note that the factor (1 + i)" is called the accumulation factor for compound interest Examples: Find the compound amount and compound interest on: 1. P10,000.00 for 5 years at 6% compounded annually. 2. P15,250.00 for 4 years and 6 months at 8% compounded semi-annually 3. P20,520.00 for 5 years and 9 months at 9% compounded quarterly 4. P25750.00 for 3 years and 5 months at 8 14 % compounded monthly Solutions: 1. Given: P= P10,000.00 6% j = 6% (m=1) or i = 7 or 6% or 0.06 n = 5 (5 years x 1 period per year) a. M = P(1 + i)" = P10,000.00 (1 + 0.06) Using scientific calculator = 10,000.00 (1+0.06) ^5 = 13,382.26 M = 13,382.26 (rounded to the nearest centavo) Note: if is not available in the calculator, use y* or xy. b. I = M-P = P13,382.26 - P10,000.00 | = P3,382.26 Hence, the compound amount is P13.382.26 and the compound interest is P3,382.26 2. Given: P= P15,250.00 8% j = 8% (m =2) or i =or 4% or 0.04 n = 9 (4 years x 2 periods per year) Note: (12 x 4 + 6 =54 x 2 = 108 + 12 = 9) or n = 9 Solution: 6 12 a. M = P(1 + i)" =P15,250.00 (1 + 0.04) M = 21,705;51 (rounded to the nearest centavo) Note: use y* or xv if is not available in the calculator. b. I = M- = P21,705.51 - P15,000.00 I = P6,455.51 as rounded off. Hence, the compound amount is P21,705.51 and the compound interest is P6,455.51. 3. Given: P = P20,520.00 9% j = 9% (m=4) or i = or 2 or 0.0225 n=5 years x 4 =23 4 9 12 Solutions: a. M = P(1 + i)" = P20,52000 (1 + 0.0225)23 M = 34,232.11 (rounded to the nearest centavo) b. I = M-P = P34,232.11 - P20,520.00 I = P13,712.11 Thus, compound amount = P34,232.11 compound interest = P13.712.11 Given: P = P25,750.25 (m = 12) or 2 11% or 0.66875% or 12 0.006875 n=3 years x 12 periods per year = 41 4. 81% j=8-% 16 5 12 Solutions: a. M = P(1 + i)" = P25,750.25 (1 + 0.006875)41 M = P34,101.96 (rounded to the nearest centavo) b. I = M-P = P34,101.96 - P25,750.25 I = P8,351.71 Thus, compound amount = P34, 101.96 compound interest=P8,351.71 Assignment #6 Finding the Principal, Rate and Time Solve the following problems. Answers must be correct to two decimal places. 1. Camby paid the bank P875.40 interest at 8% simple interest for 90 days. How much did Camby borrow? 2. Rhex borrowed P25,000.00 from a credit union. If the interest is P920.10 for 7 months, what rate of interest did he pay? Simple Discount A. Solve the given problem. Answer must be correct to two decimal places. 1. Mr. X signs a P50,000.00 note for 8 months. The banker discounts the note at 6%. Find the amount of discount and the proceeds. Compound Amount and Interest Solve the following problems. Round amounts to the nearest centavo. 11. Find the compound amount and the interest if P48,200.00 is deposited in a savings account at 8% compounded semi-annually for 3 years and 6 months