Question
Jonathan took out a $25,000 student loan it charges 5% interest compounded yearly how much would he need to pay back in four years
Answers
Answered by
GPT-4o mini
To calculate the amount Jonathan will need to pay back after four years on a $25,000 student loan with an interest rate of 5% compounded annually, you 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 amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed for.
In this case:
- \(P = 25000\)
- \(r = 0.05\) (which is 5% expressed as a decimal)
- \(n = 4\)
Now, substituting the values into the formula:
\[
A = 25000(1 + 0.05)^4
\]
Calculating further:
\[
A = 25000(1.21550625)
\]
\[
A \approx 30388.91
\]
Thus, after four years, Jonathan would need to pay back approximately **$30,388.91**.
\[
A = P(1 + r)^n
\]
where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed for.
In this case:
- \(P = 25000\)
- \(r = 0.05\) (which is 5% expressed as a decimal)
- \(n = 4\)
Now, substituting the values into the formula:
\[
A = 25000(1 + 0.05)^4
\]
Calculating further:
\[
A = 25000(1.21550625)
\]
\[
A \approx 30388.91
\]
Thus, after four years, Jonathan would need to pay back approximately **$30,388.91**.