Solve the problem.
-Find the required annual interest rate, to the nearest tenth of a percent, for $1100 to grow to $1400 if interest is compounded monthly for 7 years.
A) 0.3%
B) 3.5%
C) 2.3%
D) 6.9%

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, we have $A = 1400$, $P = 1100$, $n = 12$ (since the interest is compounded monthly), and $t = 7$. We need to find $r$.Rearranging the formula to solve for $r$, we get:$$1400 = 1100(1 + \frac{r}{12})^{12*7}$$$$1.2727 = (1 + \frac{r}{12})^{84}$$Taking the 84th root of both sides:$$1 + \frac{r}{12} = 1.2727^{1/84}$$$$\frac{r}{12} = 1.2727^{1/84} - 1$$$$r = 12(1.2727^{1/84} - 1)$$Calculating the value:$$r \approx 0.035$$ or $3.5\%$, when rounded to the nearest tenth of a percent.

Solve the Problem. -Find the Required Annual Interest Rate, to the Nearest Tenth