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Part 1

Assume you graduate from college with

​$25 comma 00025,000

in student loans. If your interest rate is fixed at

4.70%

APR with monthly compounding and you repay the loans over a

10-year

​period, what will be your monthly​ payment? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

To calculate the monthly payment on your student loan, we can use the formula for the monthly payment of a loan with compounding interest:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (in this case, $ P = 25,000 $).
- $ r $ is the monthly interest rate (which is the annual interest rate divided by 12). For an APR of 4.70%, this will be $ \frac{4.70\%}{12} $.
- $ n $ is the total number of monthly payments (which is the loan period in years multiplied by 12). Since it's a 10-year period, $ n = 10 \times 12 = 120 $.

Let's calculate this step by step.

1. The principal, $ P = 25,000 $.
2. The annual interest rate is 4.70%, so the monthly interest rate $ r = \frac{4.70\%}{12} = \frac{0.047}{12} = 0.00391667 $.
3. The total number of payments $ n = 10 \times 12 = 120 $.

Now, I will plug these values into the formula to compute $ M $.The monthly payment on your student loan will be approximately **$261.51**.

Would you like more details or have any questions?

Here are five related questions to expand on this information:
1. How does changing the loan period affect your monthly payment?
2. What would happen if the interest rate were higher or lower?
3. How does monthly compounding compare to annual compounding for loans?
4. What is the total amount repaid over the 10-year period?
5. How can early repayments reduce the interest paid?

**Tip:** Paying more than the minimum monthly payment can help reduce the overall interest and shorten the loan period.

Assume you graduate from college with $25,000 in student loans. If your interest rate is fixed at 4.70% APR with monthly compounding and you repay the loans over a 10-year period, what will be your monthly payment? (Note: Be careful not to round any intermediate steps less than six decimal places.)

Learn how to calculate the monthly payment on a $25,000 student loan with a 4.70% APR and monthly compounding over a 10-year period. This detailed solution involves using the amortization formula and understanding interest rates. Suitable for high school seniors and college students.

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