Question

clifton took out 30-year loan for $130,000 at 5.5% interest, compounded monthly. if his monthly payment on the loan is $738.13, and if $595.83 of his first payment went toward interest, how much of his second payment went toward interest?

A. $738.13
B. more than $595.83 but less than $738.13
C. $595.83
D. less than $595.83

Answer 1

To figure out how much of Clifton's second payment went toward interest, we need to understand how the monthly payment is applied to the loan balance and interest.

1. **Calculate the monthly interest rate**: The annual interest rate is 5.5%. The monthly interest rate can be calculated as:
\[
\text{Monthly Interest Rate} = \frac{5.5\%}{12} = \frac{0.055}{12} \approx 0.00458333
\]

2. **Calculate the remaining loan balance after the first payment**:
- The interest for the first month has already been calculated as $595.83.
- The total monthly payment is $738.13. The amount that goes towards the principal can be calculated as:
\[
\text{Principal Payment} = \text{Total Payment} - \text{Interest} = 738.13 - 595.83 = 142.30
\]
- The remaining loan balance after the first payment is then:
\[
\text{New Loan Balance} = 130,000 - 142.30 = 129,857.70
\]

3. **Calculate the interest for the second month**: The interest for the second month is calculated on the new loan balance:
\[
\text{Interest for Second Month} = \text{New Loan Balance} \times \text{Monthly Interest Rate} = 129,857.70 \times 0.00458333 \approx 594.52
\]

With the interest calculated for the second month being approximately $594.52, we can compare this amount to the first month's interest of $595.83.

Thus, the second month's interest is **less than $595.83**.

Given the response options, the correct answer is:

**D. less than $595.83**.