A $400 investment has doubled to $800 in six years because of a 12.25 percent return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25 percent?
A) 2.56 years
B) 2.76 years
C) 3.46 years
D) 5 years

Question

Quizplus · Accepted Answer

The investment grows according to the formula for compound interest: A = P(1 + r)^t, 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), and t is the time the money is invested for in years. Since the investment has already grown to $800, we use this as our new principal amount (P) and want to find out how long (t) it will take to grow to $1100 at the same annual interest rate of 12.25% (or 0.1225 in decimal form). Rearranging the formula to solve for t gives us t = log(A/P) / log(1 + r). Plugging in the numbers gives us t = log(1100/800) / log(1.1225), which calculates to approximately 2.76 years.

A $400 Investment Has Doubled to $800 in Six Years