Respuesta :
The formula for annual compound interest, including principal sum, is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Here, we have to find semi-annually
[tex]\begin{gathered} P=2000 \\ r=12.5\%=\frac{12.5}{100}=0.125 \\ n=2\text{ for semi-annually} \\ t=6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A=2000(1+\frac{0.125}{2})^{2\times6}=2000(1+0.0625)^{12} \\ A=2000(1.0625)^{12}=4139.77998355904\approx4139.78 \\ \therefore A=\text{ \$4139.78} \end{gathered}[/tex]Hence, the amount owed after 6 years is $4139.78.
