Question

A plastic and steel pipes and fittings company is planning to expand its business after 5 years from now. The expected money required for the expansion programme is Br. 50,000,000. The company can invest Br. 5,000,000 at the end of every year for the next five years. If the assured rate of return of investment is 18% for the company, check whether the accumulated sum in the account would be sufficient to meet the fund for the expansion programme. If not, find the difference in amounts for which the company should make some other arrangement after 5 years.

Answer 1

The objective is to find the future worth of n equal payments which are made at the end of every interest period till the end of the nth interest period at an interest rate of i compounded at the end of each interest period.

F = A[((1 + i)ⁿ – 1)/i]

F = A(F/A, i, n)

(F/A, i, n) = Equal payment series compound amount factor

A = Equal amount deposited at the end of each interest period = 5,000,000

n = Number of interest periods = 5 years

i = Interest rate = 18% or 0.18

F = Single future amount

F = 5,000,000[((1 + 0.18)⁵ – 1)/0.18]

F = 5,000,000(F/A, 18%, 5)

F = 5,000,000[((1.18)⁵ – 1)/0.18]

F = 5,000,000 × 7.1542

F = $35,771,048.80

The future sum of the annual equal payments after 5 years is equal to $35,771,048.80.

Amount needed = $50,000,000

Deficit Amount = $50,000,000 – $35,771,048.80

Deficit Amount = $14,228,951.20