Consider a loan of ​$25 comma 000 for a period of 25 years at a fixed APR of 8.5​%. Complete parts​ (a) through​ (c).
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Part 1
a. Calculate the monthly payment.
The monthly payment is ​$
  
enter your response here. 
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To calculate the monthly payment on a loan, we can use the formula for the monthly payment of a fixed-rate loan:

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

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

For this problem:
- $P = 25,000$,
- Annual interest rate = 8.5%, so the monthly interest rate is $r = \frac{8.5}{100 \times 12} = 0.007083$,
- $n = 25 \times 12 = 300$ months.

Let me calculate the monthly payment.

The monthly payment for the loan is approximately **$201.31**.

Would you like further details or have any questions? 

Here are some related questions you might find useful:
1. How would the monthly payment change if the loan period was shortened to 20 years?
2. What is the total amount paid over the life of the loan?
3. How much interest will be paid in total over the 25-year period?
4. How does changing the interest rate to 7.5% affect the monthly payment?
5. What is the impact of making extra payments on this loan?

**Tip**: A lower interest rate or shorter loan period can significantly reduce the total interest paid over the loan's lifetime.

Consider a loan of ​$25,000 for a period of 25 years at a fixed APR of 8.5%. Complete parts​ (a) through​ (c). Part 1 a. Calculate the monthly payment. The monthly payment is ​$ (Do not round until the final answer. Then round to the nearest cent as​ needed.)

Learn how to calculate the monthly payment for a $25,000 loan at a fixed 8.5% APR over a 25-year period. This problem demonstrates key financial concepts such as loan amortization and interest rate calculations. Suitable for high school students in Grades 10-12.

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