A student has a consolidated loan balance of $27,000 at the time repayment begins. The interest rate is 5.75% compounded monthly, and the repayment plan is set for 15 years. If the monthly payment is $225, rounded up to the nearest dollar, what will be the total repayment amount, including the interest paid, over the life of the loan?

To determine the total repayment amount for the student loan, including the interest paid, we need to calculate the total amount of payments made over the loan's life.

We are given the following details:
- Loan balance (Principal), $ P = 27,000 $
- Interest rate, $ r = 5.75\% $ compounded monthly
- Monthly interest rate, $ i = \frac{5.75}{100 \times 12} = 0.00479 $ (approximately)
- Loan term, $ n = 15 \times 12 = 180 $ months
- Monthly payment, $ M = 225 $ dollars

The formula for the monthly payment $ M $ on an amortized loan is:

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

Using the values, let me first check if the provided monthly payment of $ 225 $ is sufficient, and then calculate the total repayment and interest.

Let me calculate it.The expected monthly payment calculated using the loan formula is approximately **$224.21**, which is close to the rounded-up payment of **$225**. 

Since the student is paying **$225** monthly, over a period of 180 months, the total repayment amount will be:

\[
225 \times 180 = 40,500 \, \text{dollars}
\]

This means the total repayment amount, including the interest paid over the life of the loan, will be **$40,500**.

Would you like to see further details, or do you have any questions?

Here are 5 related questions you might explore:
1. How would the repayment change if the interest rate increased?
2. What if the loan term was reduced to 10 years?
3. How much interest would be saved with an extra monthly payment?
4. What is the total interest paid over the life of the loan?
5. How does compound interest affect the total repayment?

**Tip:** Making extra payments, even small ones, can significantly reduce the total interest paid over the loan's term.

This detailed solution helps calculate the total repayment amount for a student loan of $27,000 with 5.75% interest compounded monthly over 15 years. Learn how to apply the amortization formula and calculate the total payments, including interest. The monthly payment is $225, resulting in a total repayment of $40,500.

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