If I invest $20,000 at 2.5% today,how long will it take to reach a minimum of $50,000 compounded semi-annually?
A)5 years
B)37 years
C)9 and ½ years
D)17 years

Question

Quizplus · Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($20,000), r is the annual interest rate (2.5%, or 0.025), n is the number of times that interest is compounded per year (2 for semi-annually), and t is the time the money is invested for in years. We are solving for t when A is at least $50,000. Rearranging the formula to solve for t gives t = [log(A/P)] / [n*log(1 + r/n)]. Plugging in the numbers: t = [log(50,000/20,000)] / [2*log(1 + 0.025/2)] ≈ 37 years.

If I Invest $20,000 at 2