Determine the monthly payment for the following loan: a ten year loan of $25,000 with an APR of 7.2% compounded monthly 

To calculate the monthly payment for a loan, we can use the **loan amortization formula**:

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

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

### Given:
- Principal ($ P $) = $25,000
- Annual interest rate (APR) = 7.2% or 0.072
- Loan term = 10 years

### Step 1: Calculate the monthly interest rate.
\[
r = \frac{7.2\%}{12} = \frac{0.072}{12} = 0.006
\]

### Step 2: Calculate the total number of monthly payments.
\[
n = 10 \times 12 = 120
\]

### Step 3: Plug these values into the formula.
\[
M = \frac{25000 \times 0.006 \times (1 + 0.006)^{120}}{(1 + 0.006)^{120} - 1}
\]

Let me calculate this for you.The monthly payment for the loan is approximately **$292.85**.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How does changing the loan term affect the monthly payment?
2. What would be the total amount paid over the life of the loan?
3. How does compounding frequency affect the monthly payment?
4. How much interest will you pay over the life of this loan?
5. What happens if the interest rate increases to 8%?

**Tip:** When considering a loan, always factor in the total interest paid over time, not just the monthly payment.

Determine the monthly payment for the following loan: a ten-year loan of $25,000 with an APR of 7.2% compounded monthly.

Discover how to calculate the monthly payment for a $25,000 loan with an APR of 7.2% compounded monthly over 10 years. This problem explores loan amortization formulas, interest rate calculations, and exponential growth concepts. Suitable for Grades 10-12.

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