Find the payment needed to pay the following loans.

b. $9,500 at 7.25% compounded monthly for 5 years.

To find the monthly payment needed to pay off a loan, we can use the formula for the monthly payment of an amortizing loan:

\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal amount of the loan.
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12).

For this specific loan:
- $ P = 9,500 $ dollars
- Annual interest rate = 7.25%, so the monthly interest rate $ r = \frac{7.25\%}{12} = \frac{0.0725}{12} $
- Loan term = 5 years, so $ n = 5 \times 12 = 60 $ months

Let's calculate the monthly payment $ M $.The monthly payment needed to pay off the $9,500 loan at a 7.25% annual interest rate compounded monthly for 5 years is approximately **$189.23**.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How does the payment change if the interest rate increases to 8%?
2. What is the total amount paid over the 5-year period?
3. How much of the first payment goes toward interest?
4. How would bi-weekly payments affect the total interest paid?
5. What is the remaining balance after 3 years of payments?

**Tip:** Understanding how interest is compounded can significantly affect your decisions when taking out a loan.

Learn how to calculate the monthly payment required to pay off a $9,500 loan at 7.25% annual interest compounded monthly over a 5-year period. This problem involves understanding compound interest and the formula for amortizing loan payments. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation