SIMPLE INTEREST AND COMPOUND INTEREST.pptx

Business Math

1. SIMPLE AND COMPOUND INTEREST

2. Objectives . After this session, you are expected to: illustrate simple and compound interests. distinguish between simple and compound interests. compute interest, maturity value, future value, and present value in simple interest and compound interest environment. solve problems involving simple and compound interests.

3. Lender or creditor- person (or institution) who invests the money or makes the funds available Borrower or debtor- person (or institution) who owes the money or avails of the funds from the lender . .

4. Interest income derived from invested capital money paid as rental for the use of money .

5. Interest Interest (I) - a fixed rated proportion as the rate of interest for any specified time unit. Interest Rate (r) - ratio of the interest earned in one time unit to the principal. Principal or Present Value (P) - refers to the capital originally invested in a business transaction. DEPARTMENT OF EDUCATION .

6. Interest Amount / Full Amount/ Maturity or Future Value (F) - the sum of the Principal (P) and the Interest (I) due at any time after the investment of the Principal (P). Time (t) - period of coverage of the transaction. Unless otherwise specified, the time unit will be one year . DEPARTMENT OF EDUCATION .

7. Interest I = Prt where, I = interest P = Principal or original capital invested r = rate of interest (%) t = time DEPARTMENT OF EDUCATION .

8. Interest Simple Interest Compound Interest .

9. Ella and Thelma each invest P10,000 for two years, but under different schemes. Ella’s earns 2% of P10,000 the first year, which is P200, then another P200 the second year. Thelma earns 2% of P10,000 the first year, which is P200, the same as Ella’s. But during the second year, she earns 2% of the P10,000 and 2% of the P200 also.

10. Ella and Thelma each invest P10,000 for two years, but under different schemes. Ella’s earns 2% of P10,000 the first year, which is P200, then another P200 the second year. Ella invested on the simple interest. Thelma earns 2% of P10,000 the first year, which is P200, the same as Ella’s. But during the second year, she earns 2% of the P10,000 and 2% of the P200 also. Thelma invested on the compound interest.

11. Simple Interest DEPARTMENT OF EDUCATION . I = Prt F = P + I ( maturity/future value or full amount ) F = P + Prt F = P(1 + rt)

12. Simple Interest I = Prt DEPARTMENT OF EDUCATION . F = P(1 + rt)

13. Simple Interest DEPARTMENT OF EDUCATION . The unit for time ( t ) is in year ( s ). When given time ( t ) is in months, convert it to year (divide by 12). When given time ( t ) is in days, convert it to year (divide by 360 or 365).

14. Simple Interest Sample Problem. 1. Find the interest and the full amount on P3,000 at 5% interest for two years. 2. Find the principal value P and full amount F if the investment earns P200 interest in 18 months at the rate of 8%. DEPARTMENT OF EDUCATION . I = P300 F = P3,300 P = P1,666.67 F = P1,866.67

15. Simple Interest Sample Problem. 3. If P500 is the interest earned of P8,000 which was invested for 16 months, how much is the rate of interest? 4. How long will it take to accumulate P5,000 to P7,000 if the interest rate is 6%? DEPARTMENT OF EDUCATION . r = 4.70% t = 6.67 years

16. Simple Interest DEPARTMENT OF EDUCATION . When given time ( t ) is in days: Ordinary Interest - all months of the year are having 30 days, thus 360 days a year. Exact Interest - a year has exactly 365 days.

17. Simple Interest Sample Problem. 1. Find the ordinary and exact interests at 6% on P3,500 and the corresponding amounts at the end of 75 days. DEPARTMENT OF EDUCATION .

18. Compound Interest DEPARTMENT OF EDUCATION . If during the term of investment, the interest due at stated intervals is added to the principal and thereafter earns interest, the sum of the increases over the principal by the end of the term of investment is called Compound Interest .

19. Compound Interest DEPARTMENT OF EDUCATION . Compound Amount - the total amount due which consists of the principal and the compound interest. Conversion Period - the time between the successive conversions of interest into principal.

20. Compound Interest DEPARTMENT OF EDUCATION . Conversion Period - the number of unit of time in one year as basis for computing interest which could be either (a) annually, (b) semi-annualy, (c) quarterly, or (d) monthly.

21. Compound Interest DEPARTMENT OF EDUCATION . Nominal rate - refers to the rate of borrowing and is usually quoted as an annual interest rate, unless otherwise specified.

22. Compound Interest DEPARTMENT OF EDUCATION . Periodic rate or interest rate per compounding period - refers to the interest rate per conversion period. It is equal to the nominal rate divided by the compounding period in a year.

23. Compound Interest DEPARTMENT OF EDUCATION . Illustration: Solve for the compound amount and compound interest at the end of 5 years if P10,000 is invested at 6% compounded annually.

24. Compound Interest DEPARTMENT OF EDUCATION . time Principal Interest Amount 1st year 2nd year 3rd year 4th year 5th year

25. Compound Interest DEPARTMENT OF EDUCATION . time Principal (P) Interest (I) Amount (F) 1st year P10,000 P600 P10,600 2nd year 3rd year 4th year 5th year P10,600 P636 P11,236 P11,236 P674.16 P11,910.16 P11,910.16 P714.61 P12,624.77 P12,624.77 P757.49 P13,382.26

26. Compound Interest Who will earn more? Group 1 or Group 2? DEPARTMENT OF EDUCATION .

27. Compound Interest I c = F c –P c I c =Compound Interest F c = Maturity Value P c = Present Value DEPARTMENT OF EDUCATION .

28. Compound Interest Sample Problem. 1 . Solve for the compound amount and the compound interest at the end of 2 years if P1,000 is invested at 8% compounded quarterly. Solution: Data: P = P1,000 r = 8% or 0.08 m = 4 (quarterly) t = 2 (years) DEPARTMENT OF EDUCATION . F = P1,171.65 I = P171.65

29. Compound Interest Sample Problem. 2 . If P20,000 is invested for 5 years at 12% interest compounded semi-annually, find the value of F and the compound interest I. Solution: Data: P = P20,000 = 12% or 0.12 m = 2 (semi-annually) t = 5 years DEPARTMENT OF EDUCATION . F = P35,816.95 I = P15,816.95

30. Compound Interest 1 . What is the present value of P50,000 due in 7 years if money is worth 10% compounded monthly ? Solution: Data: F = P50,000 r = 10% or 0.1 m = 12 (monthly) t = 7 (term in 7 yrs.) DEPARTMENT OF EDUCATION . P = P25,657.91