Respuesta :
Solution:
Given:
[tex]\begin{gathered} P=\text{ \$25,000} \\ R=10\text{ \%} \\ T=1\text{year} \end{gathered}[/tex]To get the interest lent to his sister at 10% simple interest;
Using the simple interest formula;
[tex]\begin{gathered} I=\frac{\text{PTR}}{100} \\ I=\frac{25000\times1\times10}{100} \\ I=\text{ \$2500} \end{gathered}[/tex]
Hence, the sister will pay back $2500 interest for the money lent.
To get the interest gotten if he invests in a retirement plan at 6% compounded quarterly for a year;
Using the compound interest formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P=\text{ \$25000} \\ r=6\text{ \%=}\frac{6}{100}=0.06 \\ n=4\text{ (compounded quarterly)} \\ t=1\text{year} \\ \\ A=25000(1+\frac{0.06}{4})^{4\times1} \\ A=25000(1+0.015)^4 \\ A=25000(1.015)^4 \\ A=25000\times1.015^4 \\ A=\text{ \$26,534.09} \end{gathered}[/tex]To get the interest made from the retirement plan,
[tex]\begin{gathered} \text{Amount}=\text{principal+interest} \\ Interest=amount-pri\text{ncipal} \\ I=26534.09-25000 \\ I=\text{ \$1534.09} \end{gathered}[/tex]Hence, the interest made from the retirement plan compounded quarterly for a year is $1534.09
Thus, the additional interest the simple interest loan to his sister will generate is;
[tex]\begin{gathered} \text{Additional interest = 2500-1534.09} \\ \text{Additional interest =\$965.91} \end{gathered}[/tex]Therefore, the additional interest the simple interest loan to his sister will generate is $965.91
