Number of Periods it Takes an Investment to Grow a Certain Amount: Sally Wilson 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, Sally just won a brand new car that is worth $36,000 in a raffle. If Sally 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 Sally could retire? (Round off to the nearest 1/10 of a year)

Question

Quizplus · Accepted Answer

Using the present value formula, we can find out how many years it would take for Sally's investment to grow to $500,000 at a rate of 6.50%, compounded annually. 
PV = FV / (1 + r)^n 
$36,000 = $500,000 / (1 + 0.065)^n 
Simplifying this equation, we get: 
(1 + 0.065)^n = $500,000 / $36,000 
(1 + 0.065)^n = 13.88889 
Taking logarithms of both sides, we get: 
n * log(1 + 0.065) = log(13.88889) 
n = log(13.88889) / log(1 + 0.065) 
n ≈ 41.8 years 
Therefore, it will take Sally approximately 41.8 years to reach her retirement goal.

Number of Periods It Takes an Investment to Grow a Certain