Solve the problem.
-Find the number of years for $10,800 to grow to $14,300 at 5% compounded quarterly. Round to the nearest tenth of a year.
A) 5.6 yr
B) 4.7 yr
C) 5.5 yr
D) 6.7 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, $A = 14300$, $P = 10800$, $r = 0.05$ (5% 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:$$t = \frac{\log(14300/10800)}{4 \cdot \log(1 + 0.05/4)}$$$$t \approx 5.6$$Therefore, it takes approximately 5.6 years for $10,800 to grow to $14,300 at 5% interest compounded quarterly.

Solve the Problem. -Find the Number of Years for $10,800 to Grow to to Grow