Lesson 4 compound interest
- 2. COMPOUND INTEREST - Interest is computed on the principal and also on the accumulated past interests.Maturity (Future) Value and Compound Interest F = P(1 + r)t where; P = principal or present value F = maturity (future) value at the end of the term r = interest rate t = term/time in years The compound interest is given Example 1: Find the maturity value and the compound interest if P 10,000.00 is compounded annually at an interest rate of 2% in 5 years. Given: P = P 10,000.00 r = 2% = 0.02 t = 5 years Find: (a) maturity value F (b) compound interest Ic Solution: (a) F = P(1 + r)t (b) Ic = F - P F = (P 10,000.00)(1 + 0.02)5 Ic = P 11,040.80 – P 10,000.00 F = (P 10,000.00)(1.10408) Ic = P
- 3. Example 2: Suppose your father deposited in your bank account P 10,000.00 at an annual rate of 0.05% compounded yearly when you graduate from kindergarten and get the amount until you finish Grade 12. How much will you have in your after 12 years? Given: P = P 10,000.00 r = 0.5% = 0.005 t = 12 years Find: future value F Solution: F = P(1 + r)t F = (P 10,000.00)(1 + 0.005)12 F = (P 10,000.00)(1.0616778 F = P 10,616.78
- 4. Present Value P at Compound Interest P = F/(1 + r)t or P = F(1 + r)-t where; P = principal or present value F = maturity (future) value at end of the term r = interest rate t = term/time in years Example 3: What is the present value of P 50,000.00 due in 7 years if money is worth 10% compounded annually? Given: F = P 50,000.00 r = 10% = 0.1 t = 7 years Find: present value P Solution: (a) P = F/(1 + r)t P = P 50,000.00/(1 + 0.1)7 P = P 50,000.00)/1.9487171 P = P 25,657.91
- 5. Activity 3 Complete the table below. Use short bond paper (encoded or handwritten) Support your answers with solutions.Principal (P) Rate (r) Time (t) Compoun d Interest (Ic) Maturity Value (F) P 8% 12 years (1) (2) P 12,000.00 5.5% 6 years 9 months (3) (4) P 60,000.00 9.75% 10 months (5) (6) (7) 1% 6 years (8) P 25,000.00 (9) 7.5% 4 years (10) P
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