To calculate the accumulated value of an investment using the compound interest formulas, we will use:
- For semiannual compounding:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( P = 20000 \) (the principal)
- \( r = 0.07 \) (the annual interest rate in decimal)
- \( n = 2 \) (the number of times interest is compounded per year)
- \( t = 6 \) (the number of years)
Substituting in the values for semiannual compounding:
\[ A = 20000 \left(1 + \frac{0.07}{2}\right)^{2 \times 6} \] \[ A = 20000 \left(1 + 0.035\right)^{12} \] \[ A = 20000 \left(1.035\right)^{12} \]
Now we calculate \( (1.035)^{12} \):
\[ (1.035)^{12} \approx 1.491825 \]
Now we multiply by the principal:
\[ A \approx 20000 \times 1.491825 \approx 29836.50 \]
So the accumulated value if the money is compounded semiannually is:
\[ \boxed{29836.50} \]
1 answer