Jennifer invests $5100 in a saving certificate with an interest rate of 4.25% per year compounded monthly. How long will it take for her investment to grow to $13000? Round to the nearest tenth.
A) 1.9 years
B) 4.3 years
C) 215.6 years
D) 22.1 years
E) 211.5 years

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, 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. Here, $A = 13000$, $P = 5100$, $r = 0.0425$, and $n = 12$. We solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}$. Plugging in the values, we find that $t$ is approximately 22.1 years.

Jennifer Invests $5100 in a Saving Certificate with an Interest