Determine the monthly payment for the installment loan.
Amount Financed​ (P)
Annual Percentage Rate​ (r)
Number of Payments per Year​ (n)
Time in Years​ (t)
​$950
4.5​%
12
2
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Part 1
The monthly payment is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To determine the monthly payment for an installment loan, you can use the loan amortization formula:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (amount financed).
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of payments per year.
- $ t $ is the time in years.

Given:
- $ P = 950 $
- $ r = 4.5\% = 0.045 $
- $ n = 12 $ (monthly payments)
- $ t = 2 $ years

Let’s substitute the values and calculate the monthly payment.

\[
M = \frac{950 \cdot \frac{0.045}{12}}{1 - \left(1 + \frac{0.045}{12}\right)^{-12 \cdot 2}}
\]

Now I will calculate the result.The monthly payment for the installment loan is **$41.47**.

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

1. How does the interest rate affect monthly payments?
2. What is the total amount paid over the life of the loan?
3. How can you calculate the total interest paid on the loan?
4. What happens if the interest rate is compounded more frequently than monthly?
5. How does extending the loan term affect the monthly payment?

**Tip:** Increasing the loan term reduces monthly payments but increases the total interest paid over time.

Determine the monthly payment for the installment loan. Amount Financed​ (P) $950, Annual Percentage Rate​ (r) 4.5​%, Number of Payments per Year​ (n) 12, Time in Years​ (t) 2.

Learn how to calculate the monthly payment for a $950 loan with an Annual Percentage Rate (APR) of 4.5% over 2 years. This problem involves loan amortization, interest rate calculations, and exponential functions. Suitable for high school students in Grades 11-12 or those learning financial math.

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