Compute the compound interest.
-$5000 is invested at 9% compounded quarterly. In how many years will the account have grown to $10,500? Round to the nearest tenth of a year.
A) 8.3 yr
B) 8.6 yr
C) 1.1 yr
D) 12.1 yr

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, $A = 10500$, $P = 5000$, $r = 0.09$ (9% as a decimal), and $n = 4$ (since the interest is compounded quarterly). We need to solve for $t$.Rearranging the formula to solve for $t$, we get:$$t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}$$Substituting the given values:$$t = \frac{\log(10500/5000)}{4 \cdot \log(1 + 0.09/4)}$$$$t \approx 8.3$$ years.Therefore, it will take approximately 8.3 years for the account to grow to $10,500.

Compute the Compound Interest