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)

Question

Quizplus · Accepted Answer

We can use the future value formula to calculate how much the $36,000 will be worth in the future: FV = PV(1 + r)^n, where PV is the present value (in this case, $36,000), r is the annual interest rate (6.50%), and n is the number of years. Setting FV to $500,000 (the amount Amanda needs to retire), we can solve for n:

$500,000 = $36,000(1 + 0.065)^n
($500,000 / $36,000) = (1 + 0.065)^n
13.888 = 1.065^n
n = ln(13.888) / ln(1.065)
n = 41.81 years (rounded to the nearest 0.1 year)

Therefore, it will take Amanda approximately 41.8 years of investing the proceeds from selling her car at a 6.50% annual rate to reach her retirement goal.

Amanda Sorenson Is Planning Her Retirement