To calculate the final amount of a loan with compound interest, you can use the formula for compound interest:
\[ A = P(1 + r/n)^{nt} \]
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 time the money is invested or borrowed for, in years.
In your case:
- \( P = 5324 \) (the principal amount).
- \( r = 6.7% = 0.067 \) (annual interest rate in decimal).
- \( n = 1 \) (since it’s compounded yearly).
- \( t = 6 \) (number of years).
Plugging in these values into the formula:
\[ A = 5324 \left(1 + \frac{0.067}{1}\right)^{1 \times 6} \] \[ A = 5324 \left(1 + 0.067\right)^{6} \] \[ A = 5324 \left(1.067\right)^{6} \]
Now we calculate \( (1.067)^{6} \):
\[ (1.067)^{6} \approx 1.484812 \]
Then, multiply this result by the principal amount:
\[ A = 5324 \times 1.484812 \approx 7901.58 \]
Therefore, the final amount of the loan after 6 years would be approximately $7901.58.