Briana received a 10 year subsidized student loan of $24,000 at an annual interest rate of 4.875%. Determine her monthly payment in dollars on the loan after she graduates in 2 years. Round answer to the nearest cent.

Solution:

1. Given:

* Principal loan amount: P = 24,000 USD

* Annual interest rate: r = 0.04875

* Loan term after graduation: t = 10 years

* Monthly interest rate: r_{monthly} = \frac{r}{12} = \frac{0.04875}{12}

2. Calculate the monthly interest rate:

* r_{monthly} = \frac{0.04875}{12} = 0.0040625

3. Total number of payments or periods (months):

* n = t \times 12 = 10 \times 12 = 120

4. Use the annuity formula for monthly payments:

* M = P \times \frac{r_{monthly} \times (1 + r_{monthly})^n}{(1 + r_{monthly})^n - 1}

5. Substitute the values into the formula:

* Monthly payment, M = 24,000 \times \frac{0.0040625 \times (1 + 0.0040625)^{120}}{(1 + 0.0040625)^{120} - 1}

6. Calculate:

* M=24,000\times\frac{0.0040625\times1.62663333}{1.62663333-1}

* M=24,000\times\frac{0.006689133}{0.62663333}

* M=24,000\times0.010545

* M=253.09

7. Rounded to the nearest cent, Briana's monthly payment is:

* 253.09 USD