Find the principal that must be deposited in an account with an annual interest rate of 4%, compounded monthly, so that after 15 years the balance is $4,000. Round your answer to the nearest cent.
A)$2,197.44
B)$2,221.06
C)$2,195.32
D)$2,195.25
E)$2,201.80

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, $r$ 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. Rearranging the formula to solve for $P$, we get $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Plugging in the given values: $A = 4000$, $r = 0.04$, $n = 12$, and $t = 15$, we find the principal that needs to be deposited.

Find the Principal That Must Be Deposited in an Account