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The question asks for the monthly payments on a student loan of $15,000, with an annual interest rate of 6.8%, compounded monthly, over a period of 10 years.

To calculate this, we can use the formula for a loan payment, which is:

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

where:
- $ M $ = Monthly payment
- $ P $ = Loan principal (initial amount), which is $15,000
- $ r $ = Monthly interest rate (annual rate divided by 12 months), so $ \frac{6.8\%}{12} $
- $ n $ = Total number of payments (number of years times 12 months), so $ 10 \times 12 $

Let's calculate this step-by-step.

1. **Convert the annual interest rate to a monthly rate**:
   \[
   r = \frac{6.8\%}{12} = \frac{0.068}{12} \approx 0.005667
   \]

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

3. **Plug in the values**:
   \[
   M = \frac{15000 \times 0.005667}{1 - (1 + 0.005667)^{-120}}
   \]

Let me compute the result.The monthly payment for this loan would be approximately **$172.62**.

Would you like further details on this calculation or have additional questions?

Here are some related questions to explore:
1. How would the monthly payment change if the loan period were reduced to 5 years?
2. What would be the total interest paid over the 10-year period?
3. How does changing the compounding frequency (e.g., annually vs. monthly) affect the monthly payment?
4. What formula applies if the loan has a variable interest rate?
5. How much would you save in interest if you made additional monthly payments?

**Tip:** When dealing with compound interest, always check if the compounding period matches the payment period for accurate calculations.

At graduation, you have a student loan of $15,000. The loan has a fixed annual interest rate of 6.8%, compounded monthly, for 10 years. What will your monthly payments be? (Enter numeric answers to 2 decimal places.)

Learn how to calculate the monthly payment for a $15,000 student loan with a 6.8% annual interest rate, compounded monthly over 10 years. This problem demonstrates the use of the monthly payment formula in loan calculations, suitable for college-level students.

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