Single-Payment Compound Amount

A person deposits a sum of Rs. 20,000 at the interest rate of 18% compounded annually for 10 years. Find the maturity value after 10 years.

Solution

P = Rs. 20,000 i = 18% compounded annually n = 10 years F = P(1 + i)n = P(F/P, i, n) = 20,000 (F/P, 18%, 10) = 20,000 5.234 = Rs. 1,04,680

The maturity value of Rs. 20,000 invested now at 18% compounded yearly is equal to Rs. 1,04,680 after 10 years.

Single-Payment Present Worth Amount

A person wishes to have a future sum of Rs. 1,00,000 for his son’s education after 10 years from now. What is the single-payment that he should deposit now so that he gets the desired amount after 10 years? The bank gives 15% interest rate compounded annually.

Solution

F = Rs. 1,00,000 i = 15%, compounded annually n = 10 years P = F/(1 + i)n = F(P/F, i, n) = 1,00,000 (P/F, 15%, 10) = 1,00,000 0.2472 = Rs. 24,720

The person has to invest Rs. 24,720 now so that he will g

Equal-Payment Series Sinking Fund

A company has to replace a present facility after 15 years at an outlay of Rs. 5,00,000. It plans to deposit an equal amount at the end of every year for the next 15 years at an interest rate of 18% compounded annually. Find the equivalent amount that must be deposited at the end of every year for the next 15 years.

Solution

F = Rs. 5,00,000 n = 15 years i = 18% A = ?

The corresponding cash flow diagram is shown in Fig.

5,00,000

i = 18% 0 1       2 3 4 . . 15

A A A A A Fig. Cash flow diagram of equal-payment series sinking fund.

A = F

i (1 + i)n − 1

= F(A/F, i, n)

= 5,00,000(A/F, 18%, 15) = 5,00,000 0.0164 = Rs. 8,200

The annual equal amount which must be deposited for 15 years is Rs. 8,200.