Question
A college student takes out a $7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet) if the bank charges 3.8% interest each year?
Answers
GPT-4o mini
To find the balance of the loan after one year, you can calculate the interest on the initial loan amount and then add it to the principal.
1. **Principal amount (P)**: $7,500
2. **Interest rate (r)**: 3.8% (expressed as a decimal, this is 0.038)
3. **Time (t)**: 1 year
The formula to calculate the total balance after interest is:
\[
\text{Total Balance} = P + (P \times r \times t)
\]
Now, substitute the values into the formula:
\[
\text{Total Balance} = 7500 + (7500 \times 0.038 \times 1)
\]
Calculating the interest:
\[
7500 \times 0.038 = 285
\]
So, the total balance after one year will be:
\[
\text{Total Balance} = 7500 + 285 = 7785
\]
Thus, the balance of the loan after one year will be **$7,785**.
1. **Principal amount (P)**: $7,500
2. **Interest rate (r)**: 3.8% (expressed as a decimal, this is 0.038)
3. **Time (t)**: 1 year
The formula to calculate the total balance after interest is:
\[
\text{Total Balance} = P + (P \times r \times t)
\]
Now, substitute the values into the formula:
\[
\text{Total Balance} = 7500 + (7500 \times 0.038 \times 1)
\]
Calculating the interest:
\[
7500 \times 0.038 = 285
\]
So, the total balance after one year will be:
\[
\text{Total Balance} = 7500 + 285 = 7785
\]
Thus, the balance of the loan after one year will be **$7,785**.