Question

Compound Interest

17.) If P26,500 shall accumulate for 5 years at 7% compounded bimonthly, find the compounded interest at the end of 5 years.

18.) A sum of P 15,000 is invested now and left for eight years, at which time the principal is withdrawn. The interest has accrued and is left for another eight years. If the affective annual interest rate is 15%, what will be the withdrawal amount at the end of the 16th year?

19.) Jeffrey deposited P150 in the bank now and plans to withdraw P100 next year. What will be the amount of money left in the bank after 10 years from his withdrawal? Effective annual interest is 10%

20.) On his 4th birthday, a boy is left an inheritance. The inheritance will be paid in a lump sum of P100,000 on his 21st birthday. What is the present value of the inheritance as of the boy’s 6th birthday, if the interest is compounded annually? i = 4%

21.) An businessman wishes to accumulate a total of P 500,000 in a savings at the end of 50 years. The bank offers 1% compounded quarterly. What should be the initial deposit?

Answer 1

17) Amount deposited = 26,500

Duartion of depoit = 5 years

Interest rate = 7% compounded bi monthly which is annual effective rate of interest = [1 + (Interest rate / Number of compounding in an year)]^^{Number of compounding in an year} = [1 + (7% / 24)]^²⁴ = 1.0724 which is 7.24%

Future value of amount after 5 years = 26,500 * 1.0724^⁵ - 26,500 = 11,086.33

18) Amount Invested now = 15,000 which is left for 8 years

Annual effective rate of interest = 15%

Amount after 8 years = 15,000 * (1 + 0.15)^⁸ = 45,885.34

Amount after 16 years = 45,885.34 * (1 + 0.15)^⁸ = 140,364.3

19) Deposit amount = 150

Interest rate = 10%

Amount in account next year = 150 * 1.1 = 165

Amount withdrawed next year = 100

Amount in account after withdrawal = 165 - 100 = 65

Amount after 10 years of withdrawal = 65 * 1.1^¹⁰ = 168.60

20) Interest rate = 4%

Amount after 21st birthday = 100,000

Present value of amount on 6th birthday = [100,000 / (1 + 0.04)^¹⁵] = 55,526.45

21) Interest rate = 1% compounded quarterly whose annual effective interest rate = [1 + (1% / 4)]^⁴ = 1.0037%

Let Initial deposit be X

500,000 = X * 1.010037^⁵⁰

X = 303,454.61