Solve the problem.
-How long will it take for $1900 to grow to $2200 at an interest rate of 3.7% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.
A) 3.98 yr
B) 4.04 yr
C) 15.92 yr
D) 31.44 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, $A = 2200$, $P = 1900$, $r = 0.037$ (3.7%), 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:$$t = \frac{\log(2200/1900)}{4 \cdot \log(1 + 0.037/4)}$$$$t \approx 3.98$$ years.

Solve the Problem. -How Long Will It Take for $1900 to Grow to to Grow