To calculate how much Charmaine will owe after 8 years on her loan of $8000 at a rate of 7% compounded semiannually, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 8000 \)
- \( r = 0.07 \) (7%)
- \( n = 2 \) (since the interest is compounded semiannually)
- \( t = 8 \)
Now we can substitute these values into the formula:
\[ A = 8000 \left(1 + \frac{0.07}{2}\right)^{2 \times 8} \]
Calculating inside the parentheses first:
\[ A = 8000 \left(1 + 0.035\right)^{16} \] \[ A = 8000 \left(1.035\right)^{16} \]
Now we need to calculate \( (1.035)^{16} \):
\[ (1.035)^{16} \approx 1.747422 \]
Now substituting this value back into the equation for \( A \):
\[ A \approx 8000 \times 1.747422 \] \[ A \approx 13979.376 \]
Finally, rounding to the nearest cent:
\[ A \approx 13979.38 \]
Therefore, Charmaine will owe approximately $13,979.38 after 8 years.
1 answer