Question

You have just deposited $12,000 into an account that promises to pay you an annual interest rate of 6.7 percent each year for the next 8 years. You will leave the money invested in the account and 20 years from today, you need to have $44,950 in the account. What annual interest rate must you earn over the last 12 years to accomplish this goal?

Answer 1

FV after 8 Years = PV(1+r)^n

= $ 12000(1+0.067)^8

= $ 12000(1.067)^8

= $ 12000 * 1.6800

= 20160.28

FV after 20 Years = FV after 8 Years (1+r)^12

44950 = 20160.28 (1+r)^12

(1+r)^12 = 44950 / 20160.28

= 2.2296

1+r = 2.2296^(1/12)

= 1.0691

r = 1.0691 - 1

= 0.0691 i.e 6.91%