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Let's focus on solving part (b) of this problem related to the private loan.

The private loan details are as follows:
- Principal (Loan Amount): $4400
- Interest rate: 7.5% (annual)
- Loan term: 10 years

To find the monthly payment on this private loan, we can use the loan amortization formula:

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

Where:
- $M$ = Monthly payment
- $P$ = Principal ($4400)
- $r$ = Monthly interest rate = Annual interest rate / 12 = 7.5% / 12
- $n$ = Number of payments = Loan term in years $\times$ 12

I'll calculate this for you.The monthly payment on the private loan is approximately $52.23.

Would you like any further details or explanations? Here are some follow-up questions:

1. How does changing the loan term affect the monthly payment?
2. What happens if the interest rate increases on the private loan?
3. How is the total interest paid over the loan term calculated?
4. What are the key differences between federal and private student loans?
5. How does capitalizing interest affect the loan?

**Tip:** Always compare loan terms and interest rates before taking out a loan to ensure you choose the most affordable option in the long run.

Pat receives a series of four annual federally subsidized student loans, each for $5200 at 6.7%. To defray rising costs for her senior year, 3 years after acquiring the first loan, she takes out a private student loan for $4400 at 7.5% interest with a term of 10 years and capitalizes the interest for her last year of college. She graduates 9 months after getting the private loan. Payments on all loans are deferred until 6 months after graduation. Find her monthly payment. (Part b) Find the monthly payment on the private loan. Round your answer to two decimal places, if necessary.

Learn how to calculate the monthly payment on a $4400 private student loan with a 7.5% annual interest rate and a term of 10 years. This problem uses the loan amortization formula and covers key financial mathematics concepts. Suitable for students in Grades 10-12.

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