Determine the monthly payment for the installment loan. Amount Financed​ = $750 Annual Percentage Rate​ = 9% Number of Payments per Year​ = 12 Time in Years​ ​= 2

To determine the monthly payment for the installment loan, we can use the following formula for the monthly payment of a 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 (amount financed).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (number of payments per year multiplied by the time in years).

### Given:
- Amount Financed $ P = 750 $
- Annual Percentage Rate $ \text{APR} = 9\% = 0.09 $
- Number of Payments per Year = 12
- Time in Years = 2

### Step 1: Calculate the monthly interest rate $ r $

\[
r = \frac{\text{APR}}{12} = \frac{0.09}{12} = 0.0075
\]

### Step 2: Calculate the total number of payments $ n $

\[
n = \text{Number of Payments per Year} \times \text{Time in Years} = 12 \times 2 = 24
\]

### Step 3: Calculate the monthly payment $ M $

\[
M = \frac{750 \times 0.0075 \times (1 + 0.0075)^{24}}{(1 + 0.0075)^{24} - 1}
\]

Let's compute this value:

\[
M = \frac{750 \times 0.0075 \times (1.0075)^{24}}{(1.0075)^{24} - 1}
\]

\[
M \approx \frac{750 \times 0.0075 \times 1.196682}{1.196682 - 1}
\]

\[
M \approx \frac{6.742\text{ (rounded)}}{0.196682}
\]

\[
M \approx 34.30
\]

So, the monthly payment $ M $ is approximately **$34.30**.

Would you like to go into more detail about any of the calculations? 

Here are some related questions for further exploration:
1. What would be the monthly payment if the loan amount was $1,000?
2. How does the monthly payment change if the interest rate is 8% instead of 9%?
3. What is the total interest paid over the 2 years?
4. How much would the monthly payment be for a 3-year term with the same amount financed and interest rate?
5. What is the total cost of the loan after 2 years?
6. How does changing the number of payments per year affect the monthly payment?
7. What would be the monthly payment if the amount financed was $750 but the loan term was only 1 year?
8. How does an increase in the loan term affect the total interest paid?

**Tip:** Lowering the loan term decreases the total interest paid over time but increases the monthly payment.

Learn how to calculate the monthly payment for an installment loan of $750 with a 9% APR over a 2-year period. Step-by-step solution using the installment loan monthly payment formula. Suitable for anyone looking to understand loan payment calculations.

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