Select the correct answer.

Jenny borrowed [tex] \$500 [/tex] for five years at 4 percent interest, compounded annually. What is the total amount she will have paid when she pays off the loan?

Total amount [tex] = P(1 + i)^t [/tex]

A. [tex] \$608.33 [/tex]
B. [tex] \$729.99 [/tex]
C. [tex] \$765.77 [/tex]



Answer :

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