Simple and Compound Interest - General Mathematics

PPT about Simple and Compound interest topic in General Mathematics

1. OBJECTIVES Define compound interest Illustrate compound interest Compute interest, maturity value, and present value in compound interest, and Solve problems involving compound interest.

2. REVIEW The simple interest (I) on the principal (P) at the rate (r) per year for t years is:  

3. REVIEW The simple interest on the loan of at 8% for 3 years is:  

4. REVIEW Maturity Value (A)  

5. COMPOUND INTEREST Compound interest ( ) When the interest due at the end of a certain period is added to the principal and that sum earns interest for the next period, the interest paid is called compound interest.  

6. EXAMPLE Due to COVID-19 pandemic Miss Dada a female resident of Brgy . May Pagkakaisa somewhere in Quezon Province thinks of a business that can provide for her needs as well as the need of her neighbors so she can be of help even in this trying time. she doesn’t have money on hand, she decided to borrow from a bank with a start-up capital of ₱50,000.00 at 7% interest rate compounded annually and payable within 5 years . Compute for the interest yield.

7. Time (t) Amount at the start of year t Interest Rate (r) Compound Interest Amount at the end of year t (maturity value) Solution Answer 1 50,000 7% 3,500 50,000 + 3,500 = 53,500 2 53,500 7% 3,745 53,500 + 3,745 = 57,245 3 57,245 7% 4,007.15 61,252.15 4 61,252.15 7% 4,287.65 65,539.80 5 66,079.80 7% 4,587.79 70,125.39 Time (t) Amount at the start of year t Interest Rate (r) Compound Interest Amount at the end of year t (maturity value) Solution Answer 1 50,000 7% 3,500 50,000 + 3,500 = 53,500 2 53,500 7% 3,745 53,500 + 3,745 = 57,245 3 57,245 7% 4,007.15 61,252.15 4 61,252.15 7% 4,287.65 65,539.80 5 66,079.80 7% 4,587.79 70,125.39 SOLUTION

8. SOLUTION Maturity Value (A)  

9. FORMULAS COMPOUND ANNUALLY COMPOUND SEMIANNUALLY  

10. FORMULAS COMPOUND QUARTERLY COMPOUNDING K TIMES PER YEAR  

11. EXAMPLE Find the compound amount of ₱ 35,000 at 15% compound semiannually for 12 years.

12.     P = ₱ 35,000, r = 15% or 0.15, t = 12        

13. EXAMPLE Find the compound amount on deposit at the end of 4 years if ₱20,000.00 is deposited at 4% compounded semiannually.

14. EXAMPLE If ₱ 320,000.00 is invested for 5 years at 8% compounded quarterly, find ( a ) the compound amount and ( b ) the compound interest.

15. EXAMPLE Find the maturity value and interest if ₱ 10,000 is deposited in a bank at 2% compounded quarterly for 5 years.

16. EXAMPLE Find the maturity value and interest if ₱ 10,000 is deposited in a bank at 2% compounded monthly for 5 years.

17. EXAMPLE Cris borrows ₱ 50,000 and promise to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years?

18. EXAMPLE what amount must be invested to have ₱ 128,376.52 after 8 years if money is worth 6% compounded semi-annually?

19. EXAMPLE What is the present value of ₱ 25,000 due in 2 years and 6 months if money is worth 10% compounded quarterly?