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Interest

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interest compound interst and annuities.

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• Interest

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4. 4. Interest 4
5. 5.        The amount paid at stated rate for use of money for specific time. we can also say that the rent.Simple interest is most often used for loans of shorter duration. Charge of borrowed money at annual percentage rate is interest. The money borrowed in a loan is called the principal. The number of dollars received by the borrower is the present value. In a simple interest loan, the principal and present value are the same. The interest rate is the fee for a simple interest loan and usually is expressed as a present of the principal. Simple interest is paid on the principal borrowed and not paid on interest already earned. 5
6. 6. The simple interest of a loan can be calculated using the following formula. P = principal (amount borrowed) r = interest rate per year (in decimal form) t = time in years. 6
7. 7.  Find simple interest on an amount of Rs 800 in 8 month’ As we know formula I= 800*.05*8/12= 26.67 answer Hence interest is 26.67 7
8. 8. An individual borrows \$300 for 6 months at 1% simple interest per month. How much interest is paid? Remember to check that r and t are consistent in time units. Here, it will be months. I = Prt = 300 0.01 6 = \$18 Assume you invest \$1,000 at 6% simple interest for 3 years. (\$1,000 .06 3 = \$180) (or \$60 each year. You would earn \$180 interest. for 3 years) 8
9. 9. where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years). The formula can also be expressed as: 9
10. 10.  A loan made at simple interest requires that the borrower pay back the sum borrowed (principal) plus the interest. This total is called the future value, or amount and is equal to P + I.    where   P + Prt P(1 + rt) P = principal or present value r = annual interest rate (in decimal form) t = time in years A = amount or future value 10
11. 11. Find the future value of \$460 in 8 months, if the annual interest rate is 12%. A = P (1 + rt ) If you can earn 6% interest, what lump sum must be deposited now so that its value will be \$3500 after 9 months? A = P (1 + rt ) 11
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13. 13.  Interest paid on principal plus interest is called compound interest it can be done semiannually, quarterly, monthly, or daily. This time interval is called the compounding period (or the period). Compound interest is based on the principal which changes from time to time  The unpaid interest is added to the principal balance and becomes part of the new principal balance for the next interest period.  13
14. 14. Period Interest Credited Times Credited per year 1 Rate per compounding period R Annual year Semiannual 6 months 2 R 2 Quarterly quarter 4 R 4 Monthly month 12 R 12 14
15. 15. Amount : Compound Interest  Where and  A = amount or future value at the end of n periods  P = principal or present value  r = annual nominal rate  m = number of compounding periods per year  i = rate per compounding period  n = total number of compounding periods 15
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17. 17.  Suppose \$800 is invested at 6%, and it is compounded annually. What is the amount in the account at the end of 4 years? ` First, determine the information that is given  There will be \$1009.98 in the account after 4 years.  17
18. 18.  The general formula for finding the amount after a specified number of compound periods is where r = annual interest rate  m = number of times compounded per year  i = r/m = interest rate per period  n = mt, the number of periods, where t is the number of years  A = amount (future value) at the end of n compound periods  P = principal (present value) 18
19. 19.  Interest earned on the principal investment   Earning interest on interest Principal plus interest 19
20. 20. the difference between simple interest and compound interest on a certain sum is Rs 250for two years at 5% P.a find the sum? T= 2 years R=.05 P=? I=PRT P=.05*2 I=.10 C.I=P(1+I^N)-1 C.I=10(1+.05^2)-1 C.I=.1025 C.I –S.I 0.1025-.10=.0025 250/.0025=10000 The sum is 10000 20
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22. 22. a sequence of payments made at regular time intervals. payments made at the end of each payment period. payment period coincides with the interest conversion period. 22
23. 23.  The future value S of an annuity of n payments of R dollars each, paid at the end of each investment period into an account that earns interest at the rate of i per period is S R (1 i) n 1 i 23
24. 24.  The present value P of an annuity of n payments of R dollars each, paid at the end of each investment period into an account that earns interest at the rate of i per period is P R 1 (1 i) n i 24
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