Briana received a 10-year subsidized student loan of $22,000 at an annual interest rate of 4.125%. Determine her monthly payment (in dollars) on the loan after she graduates in 2 years. (Round your answer to the nearest cent.)

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?

---

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.

Find out how to calculate the monthly payment for a $22,000 student loan with a 4.125% interest rate over a 10-year period. This detailed guide includes step-by-step instructions for using the amortized loan formula. Suitable for high school and college-level students studying financial mathematics.

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