To calculate the total amount that Jonathan will need to pay back after four years, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial loan amount).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is borrowed for.
In this case:
- \( P = 25,000 \)
- \( r = 0.05 \)
- \( n = 4 \)
Substituting in the values:
\[ A = 25000(1 + 0.05)^4 \]
Calculating \( (1 + 0.05)^4 \):
\[ (1 + 0.05)^4 = 1.21550625 \]
Now multiply this value by the principal:
\[ A = 25000 \times 1.21550625 \]
Calculating the total amount:
\[ A \approx 30387.66 \]
Therefore, after rounding to two decimal places, Jonathan will need to pay back:
\[ \text{Total amount} = $30,387.66 \]
So, the final answer is $30,387.66.