To determine Briana's monthly payment after she graduates, we can treat this as a standard amortized loan calculation with a fixed monthly payment. Here are the key details provided:

• Loan amount $(P)$: $22,000
• Annual interest rate: 4.125%
• Loan term: 10 years (120 months)

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

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

where:

• $P$ is the loan principal ($22,000),
• $r$ is the monthly interest rate (annual rate divided by 12),
• $n$ is the total number of payments (120 months for 10 years).

Step-by-Step Calculation

1. Convert the annual interest rate to a monthly rate: $r = \frac{4.125\%}{12} = 0.0034375$

2. Determine the total number of monthly payments: $n = 10 \times 12 = 120$

3. Plugging values into the formula:

   $M = \frac{22000 \times 0.0034375 \times (1 + 0.0034375)^{120}}{(1 + 0.0034375)^{120} - 1}$

After calculating this, Briana’s monthly payment $M$ will be approximately:

$M \approx 224.32$

Answer

Briana's monthly payment after she graduates will be $224.32.

Would you like a breakdown of each calculation step or further explanation?

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1. How would the monthly payment change if the interest rate were slightly higher, such as 4.5%?
2. What would Briana's total interest paid be over the 10 years?
3. How would the monthly payment change if she decided to pay off the loan in 5 years instead?
4. How would an unsubsidized loan affect Briana’s payment schedule if interest accrued during the 2 years of school?
5. What would be the impact of a larger loan amount, such as $30,000, at the same interest rate?

Tip: For any loan, a lower interest rate or shorter loan term will decrease the total interest paid over time.