Borrows 2500 loan at 13.2 PA, compounding monthly and is intended to repaid with 5 equal monthly repayments

to find how much he has to pay monthly

To find the monthly payment for a loan compounded monthly, we can use the formula for the monthly payment of an installment loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (in this case, $2,500).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the number of payments (in this case, 5).

Let's calculate the monthly payment.

### Step 1: Convert the annual interest rate to a monthly interest rate
\[
r = \frac{13.2\%}{12} = \frac{0.132}{12} \approx 0.011
\]

### Step 2: Calculate the monthly payment using the formula
\[
M = \frac{2500 \times 0.011 \times (1 + 0.011)^5}{(1 + 0.011)^5 - 1}
\]

I'll calculate this next.The monthly payment required to repay the loan is approximately **$516.62**.

Would you like more details or have any questions?

Here are five related questions to explore:
1. How does the monthly payment change if the interest rate is lower?
2. What would be the monthly payment for a 12-month repayment period instead of 5 months?
3. How much total interest will be paid over the life of the loan?
4. How would the calculation change if the loan compounded quarterly instead of monthly?
5. What happens to the monthly payment if the loan amount increases to $5,000?

**Tip:** Understanding how to convert between annual and monthly interest rates is key when working with loans and compounding.

Learn how to calculate monthly loan repayment for a $2500 loan at 13.2% annual interest rate, compounded monthly and repaid over 5 months. Get a detailed step-by-step solution with the monthly payment formula for installment loans.

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