Question

If $163,300 is invested in an account earning 3.75% annual interest compounded semi-annually, how much interest is accrued in the first 4 years? Round to the nearest cent?

Answer 1

Solution:

An amount compounded is given as;

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where;} \\ P=\text{ amount invested;} \\ r=\text{ interest rate;} \\ n=\text{ number of times interest applied per time period;} \\ t=\text{ number of time period elapsed.} \end{gathered}$

Given that;

$\begin{gathered} P=163,300 \\ r=0.0375 \\ n=2 \\ t=4 \end{gathered}$

Thus, we have;

$\begin{gathered} A=163300(1+\frac{0.0375}{2})^{2\times4} \\ A=163300(1.01875)^8 \\ A=189464.20 \end{gathered}$

Thus, the interest accrued in the first 4 years is;

$\begin{gathered} I=A-P \\ I=189464.20-163300 \\ I=26164.20 \end{gathered}$

FINAL ANSWER: $26,164.20