Question

How would you calculate the final amount of a 6 year loan of 5324 with a compound interest rate of 6.7 compounded yearly?

Answer 1

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**.