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 has the additional funds she needs to reach her goal? (Round off to the nearest 1/10 of a year)

Question

Quizplus · Accepted Answer

We can use the formula:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

In this case, PV = $36,000 and we want to find n. Our target future value is $500,000 - the amount Amanda needs to reach her retirement goal.

$500,000 = $36,000 x (1 + 0.065)^n
Dividing both sides by $36,000:
13.89 = 1.065^n

Taking the natural logarithm of both sides:
ln(13.89) = n x ln(1.065)
n = ln(13.89) / ln(1.065)
n ≈ 41.8

Therefore, it will take Amanda about 41.8 years to reach her retirement goal by investing the proceeds from selling her car. The answer is B.

Amanda Sorenson Is Planning Her Retirement