Question

If $7300 is invested in a savings account for which interest is compounded monthly, and if the $7300 turns into $8600 in 2 years, what is the interest rate of the savings account? A.16.50% B.8.22% C.4.10% D.5.48%

Answer 1

Using the formula for compound interest we get
\[8600=7300(1+\frac{r}{12})^{2\times 12}\]
\[\frac{8600}{7300}=(1+\frac{r}{12})^{24}\]
Taking natural logs of both sides gives
\[\frac{\ln \frac{8600}{7300}}{24}=\ln (1+\frac{r}{12})\]
Simplifying, we get
\[\ln (1+\frac{r}{12})=0.00682866\ .........(1)\]
Now you just need to solve equation (1) to find the interest rate r as a decimal. Multiply the value of r by 100 to find the percentage interest rate.

Answer 2

B. 8.22%