Simon took out an unsubsidized student loan of $43,000 at a 2.4% APR, compounded monthly, to pay for his last six semesters of college. If he will begin paying off the loan in 33 months with monthly payments lasting for 20 years, what will be the amount of his monthly payment?

To calculate Simon's monthly payment on his unsubsidized student loan, we can use the formula for the monthly payment of a loan based on compound interest, which is typically represented as:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal amount of the loan.
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the number of total payments (the number of months for repayment).

### Given:
- Principal, $ P = 43,000 $ dollars.
- Annual interest rate, APR = 2.4% (which is 0.024 as a decimal).
- Monthly interest rate, $ r = \frac{0.024}{12} = 0.002 $.
- The loan will be paid off in 20 years, so $ n = 20 \times 12 = 240 $ months.

Now, we can calculate the monthly payment. Let me compute this for you.Simon’s monthly payment will be approximately **$225.77**.

Do you want more details or have any further questions?

Here are 5 related questions to expand on this concept:
1. How much total interest will Simon pay over the 20-year period?
2. What would Simon's monthly payment be if the interest rate were 3% instead of 2.4%?
3. How much would Simon save in interest if he paid off the loan in 15 years instead of 20?
4. What is the total amount Simon will pay over the life of the loan?
5. How does the frequency of compounding (e.g., quarterly vs. monthly) affect Simon's payments?

**Tip:** Always verify whether interest is compounded monthly, annually, or differently, as it significantly affects the total payment.

Learn how to calculate the monthly payment on a $43,000 unsubsidized student loan with a 2.4% APR, compounded monthly. This problem explores key mathematical concepts like loan amortization and compound interest, ideal for students at the high school or college level.

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