SOLUTION
The simple interest is caculated using the formula
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{ Principal} \\ \text{Where } \\ \text{ Principla=initial payment } \\ \text{Amount = future value } \end{gathered}[/tex]From the question, we have
[tex]\begin{gathered} P=25,000 \\ \text{rate r=6\%=0.06} \\ \text{time t=4years} \\ n=\text{ number of years=2 compounded semiannually} \end{gathered}[/tex]Using the formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute the value into the formula, we have
[tex]\begin{gathered} A=25,000(1+\frac{0.06}{2})^{2\times4} \\ \text{Then} \\ A=25,000(1+0.03)^8 \\ A=25,000(1.03)^8 \\ A=25,000\times1.2668=31\text{ 669.252} \end{gathered}[/tex]Hence
Amount = 31, 669.25203
Then the interest becomes
[tex]\text{ Interest=31 669.25203-25 000=6 669.2520}[/tex]Hence
The interest after four years will be 6, 669.25
