Jeffery Wei received a 6-year non-subsidized student loan of $30,000 at an annual interest rate of 5.5%. What are Jeffery's monthly loan payments for this loan after he graduates in 4 years? (Round your answer to the nearest cent.)

To determine Jeffery Wei's monthly loan payments after he graduates, we need to use the formula for the monthly payment on an amortizing loan. The formula is:

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

where:
- $ M $ is the monthly payment
- $ P $ is the principal loan amount (\$30,000)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the number of payments (loan term in years times 12)

First, we calculate the monthly interest rate:

\[ r = \frac{5.5\%}{12} = \frac{0.055}{12} = 0.0045833 \]

Next, we calculate the total number of payments:

\[ n = 6 \text{ years} \times 12 \text{ months/year} = 72 \text{ payments} \]

Now, we can plug these values into the formula:

\[ M = \frac{30000 \cdot 0.0045833 \cdot (1 + 0.0045833)^{72}}{(1 + 0.0045833)^{72} - 1} \]

First, calculate $(1 + r)^n$:

\[ (1 + 0.0045833)^{72} \approx 1.340095 \]

Next, calculate the numerator:

\[ 30000 \cdot 0.0045833 \cdot 1.340095 \approx 184.235 \]

Then, calculate the denominator:

\[ 1.340095 - 1 = 0.340095 \]

Finally, divide the numerator by the denominator to find $ M $:

\[ M = \frac{184.235}{0.340095} \approx 541.66 \]

So, Jeffery's monthly loan payment is approximately $ \$541.66 $.

Do you want any details or have any questions about this calculation?

Here are some related questions:
1. What is the total amount Jeffery will pay over the life of the loan?
2. How much interest will Jeffery pay over the life of the loan?
3. What would the monthly payment be if the interest rate was 4.5% instead?
4. How does the loan term affect the monthly payments?
5. What is the impact of making extra payments on the loan?
6. How does the principal amount affect the monthly payment?
7. What would be the monthly payment if the loan term was 10 years instead of 6 years?
8. What is the formula for calculating the monthly payment on a student loan?

**Tip:** Always compare loan offers and their terms, including interest rates and repayment periods, to find the best option for your financial situation.

Learn how to calculate Jeffery Wei's monthly student loan payments after graduation with a detailed step-by-step solution. This problem involves interest calculation and amortization concepts. Suitable for advanced high school students studying financial mathematics.

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