Question

Faisal has$ 15000 in his savings account and can save an additional$ 4500 per year. If interest rates are​ 12%, how long will it take his savings to grow to$50,000​?

A. 5.5 years
B. 4.5 years
C. 6.5 years
D. 3.5 years

Answer 1

B. 4.5 years

Step-by-step explanation:

Present value = $15000

Annual saving (annuity) = $4500

Interest rate = 12% or 0.12

Future value = $50000

We have given present value, annuity amount, and the future value. Now time taken is required to find out. Use the below formula to find the time taken.

Future value = Annuity [((1 + r)^n – 1) / r] + PV(1+r)^n

50000 = 4500 [((1 + 0.12)^n – 1) / 0.12] + 15000(1 + 0.12)^n

50000 = 37500 (1.12^n – 1) + 15000*1.12^n

n = 4.5

Thus, the number of years needed is 4.5 years.