How many years will it take for $500 to grow to $1,039.50 if it is invested at 5% compounded annually?
A) 15
B) 14
C) 13
D) 12

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 (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, we are solving for t, the time in years, with A = $1,039.50, P = $500, r = 5% or 0.05, and n = 1 (since the interest is compounded annually). Rearranging the formula to solve for t gives us t = log(A/P) / n[log(1 + r/n)]. Plugging in the values gives us t = log(1,039.50/500) / log(1.05), which calculates to approximately 15 years.

How Many Years Will It Take for $500 to Grow