How long will it take for $800 to grow to $1300 at an interest rate of 5.6% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.
A) 8.91 yr
B) 34.92 yr
C) 8.73 yr
D) 29.22 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, $A = 1300$, $P = 800$, $r = 0.056$, and $n = 4$ (since the interest is compounded quarterly). We solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{n\log(1 + r/n)}$. Substituting the given values, $t = \frac{\log(1300/800)}{4\log(1 + 0.056/4)}$, which approximately equals 8.73 years.

How Long Will It Take for $800 to Grow to $1300