Angelo borrow $8000 from his credit ,he agree to repay loan by making equal monthly payment for 5 year .interest is 9% compunded monthly . What is size of monthly payment

To calculate the size of the monthly payment for Angelo's loan, we need to use the formula for the monthly payment on an amortizing loan, which is given by:

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

Where:
- $M$ is the monthly payment.
- $P$ is the principal amount of the loan (in this case, $8000).
- $r$ is the monthly interest rate (annual rate divided by 12).
- $n$ is the total number of payments (number of years multiplied by 12).

### Step-by-Step Solution:

1. **Identify the values:**
   - Principal amount, $P = 8000$ dollars.
   - Annual interest rate, $9\%$, so the monthly interest rate $r = \frac{9\%}{12} = \frac{0.09}{12} = 0.0075$.
   - Total number of payments, $n = 5 \times 12 = 60$ months.

2. **Substitute the values into the formula:**

\[
M = \frac{8000 \times 0.0075(1 + 0.0075)^{60}}{(1 + 0.0075)^{60} - 1}
\]

3. **Calculate the monthly payment:**

Let's calculate it step by step:

\[
(1 + r)^{60} = (1 + 0.0075)^{60}
\]

\[
(1.0075)^{60} \approx 1.5116
\]

\[
M = \frac{8000 \times 0.0075 \times 1.5116}{1.5116 - 1}
\]

\[
M = \frac{8000 \times 0.011337}{0.5116} 
\]

\[
M \approx \frac{90.696}{0.5116} \approx 177.32 \text{ dollars}
\]

### Final Answer:

Angelo's monthly payment would be **$177.32**.

Would you like further details on this calculation or assistance with another problem? Here are some related questions that might interest you:

1. How does compounding frequency affect the total interest paid on a loan?
2. What would Angelo's monthly payment be if the interest rate were compounded quarterly instead of monthly?
3. How would the monthly payment change if the loan term were 3 years instead of 5 years?
4. Can you explain the difference between simple interest and compound interest in loan calculations?
5. What is the total amount Angelo will pay over the life of the loan?
6. How much interest will Angelo pay in total over the 5 years?
7. What would the monthly payment be if the interest rate were 12% instead of 9%?
8. How can Angelo reduce the amount of interest he pays over the life of the loan?

**Tip:** Always double-check the loan terms, especially the compounding frequency and interest rate, as they significantly impact the monthly payments and total interest paid.

Learn how to calculate Angelo's monthly loan payment with an $8000 principal, 9% annual interest compounded monthly, and a repayment period of 5 years. Detailed step-by-step solution provided.

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