Questions: When Debra had 2 years left in college, she took out a student loan for 12,130. The loan has an annual interest rate of 8.7%. Debra graduated 2 years after acquiring the loan and began repaying the loan immediately upon graduation. According to the terms of the loan, Debra will make monthly payments for 5 years after graduation. During the 2 years she was in school and not making payments, the loan accrued simple interest. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) If Debra's loan is subsidized, find her monthly payment. Subsidized loan monthly payment: (b) If Debra's loan is unsubsidized, find her monthly payment. Unsubsidized loan monthly payment:

Solution Steps

For the subsidized loan, no interest accrues while Debra is in school. The monthly payment \( M \) can be calculated using the formula: \[ M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \] where:

• \( P = 12130 \)
• \( r = \frac{0.087}{12} \approx 0.00725 \)
• \( n = 5 \times 12 = 60 \)

Substituting the values, we find: \[ M \approx 250.04 \]

For the unsubsidized loan, interest accrues during the 2 years Debra is in school. The total amount \( A \) after 2 years can be calculated using simple interest: \[ A = P \cdot (1 + rt) \] where:

• \( P = 12130 \)
• \( r = 0.087 \)
• \( t = 2 \)

Calculating this gives: \[ A \approx 14240.62 \]

Using the total amount \( A \) calculated above, we can find the monthly payment for the unsubsidized loan using the same formula: \[ M = \frac{A \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \] Substituting the values: \[ M \approx 293.54 \]

Final Answer