To determine the total amount Jenny will pay off after borrowing \[tex]$500 for five years at an annual interest rate of 4%, compounded annually, we use the compound interest formula:
\[
A = P(1 + i)^t
\]
Where:
- \( P \) is the principal amount (initial amount of money), which is \$[/tex]500.
- [tex]\( i \)[/tex] is the annual interest rate (expressed as a decimal), which is 0.04.
- [tex]\( t \)[/tex] is the time in years, which is 5 years.
Let's go step-by-step through the calculation:
1. Identify the principal amount:
[tex]\[ P = \$500 \][/tex]
2. Convert the interest rate to a decimal:
[tex]\[ i = 4\% = 0.04 \][/tex]
3. Determine the number of years:
[tex]\[ t = 5 \][/tex]
4. Apply the values to the compound interest formula:
[tex]\[
A = 500 \times (1 + 0.04)^5
\][/tex]
5. Calculate the expression inside the parentheses:
[tex]\[
1 + 0.04 = 1.04
\][/tex]
6. Raise 1.04 to the power of 5:
[tex]\[
(1.04)^5
\][/tex]
7. Compute the total amount:
[tex]\[
A = 500 \times (1.04)^5
\][/tex]
Based on the calculations, the total amount Jenny will have to pay off the loan after 5 years is approximately:
[tex]\[
A \approx 608.33
\][/tex]
So, the correct answer is:
A. \$ 608.33
