Solve the problem. Round your answer to the nearest cent.
-John Lee's savings account has a balance of $\$ 774$. After 4 years, what will the amount of interest be at $4 \%$ compounded semiannually?
A) $\$ 131.47$
B) $\$ 63.80$
C) $\$ 132.86$
D) $\$ 123.84$

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 (initial investment), $r$ 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. For this problem, $P = \$774$, $r = 4\% = 0.04$, $n = 2$ (since interest is compounded semiannually), and $t = 4$ years. Plugging these values into the formula gives $A = 774(1 + \frac{0.04}{2})^{2*4}$. Calculating this gives $A ≈ \$906.86$. The interest earned is the final amount minus the initial investment, so the interest is $906.86 - 774 = \$132.86$.

Solve the Problem $774\$ 774$774 After 4 Years, What Will the Amount of Interest

Solve the Problem $\$ 774$ After 4 Years, What Will the Amount of Interest