What monthly payment is required to amortize a loan of $50,000 over 12 years if interest at the rate of 9%/year is charged on the unpaid balance and interest calculations are made at the end of each month?

To calculate the monthly payment required to amortize a loan of $50,000 over 12 years with an annual interest rate of 9%, we use the **loan amortization formula** for fixed monthly payments:

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

Where:
- $M$ = Monthly payment
- $P$ = Principal (loan amount) = $50,000
- $r$ = Monthly interest rate = $\frac{9\%}{12} = 0.0075$
- $n$ = Total number of payments = 12 years $\times$ 12 months/year = 144

Now let's plug in the values and compute $M$.The monthly payment required to amortize the loan of $50,000 over 12 years with a 9% annual interest rate is approximately **$569.02**.

Would you like further details or have any questions? Here are some related questions:

1. How does the monthly interest rate affect the monthly payment?
2. What happens to the total interest paid if the loan period is extended to 15 years?
3. How would the payment change with a different interest rate, say 6%?
4. What is the total amount paid over the entire loan period?
5. Can you explain how the balance decreases each month?

**Tip:** In loan amortization, the earlier payments are weighted more toward interest, while later payments reduce the principal faster.

Find out how to calculate the monthly payment needed to amortize a $50,000 loan over 12 years with a 9% annual interest rate. This step-by-step guide explains the loan amortization formula and breaks down key concepts in financial mathematics. Ideal for college students or anyone studying loan amortization.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation