Question

Amanda Sorenson is planning her retirement. She is presently investing in a 401(k) but needs an additional $500,000 to reach her retirement goal. As luck would have it. Amanda just won a brand new car that is worth $36,000 in a raffle. If Amanda were to sell the car and invest the $36,000 proceeds at a rate of 6.50%, compounded annually, how long will it be before Amanda could retire? (Round off to the nearest 1/10 of a year) 36.6 years O41.8 years O24.0 years 52.2 years

Answer 1

It will take 41.8 years.

Calculation :-

A = 500,000, P = 36,000, r = 6.50%, n = 1

500,000 = 36,000(1 + 0.065/1)^{1 x t}

(1.065)^1xt = 500,000/36,000

(1.065)^1xt = 13.88889

Taking natural log both sides

In(1.065^1xt) = In(13.88889)

1 x t x In(1.065) = In(13.88889)

t = In(13.88889)/In(1.065)

t = 41.78 = 41.8 years