How Much Greater will Jessica's Monthly Payment Be?

Question:

How much greater will Jessica’s monthly payment be if the loan is unsubsidized than if the loan is subsidized?

Options:

A. $36.98 B. $23.07 C. $37.67 D. $166.37

Answer:

The correct statement is that the monthly payment of Jessica will be greater by approximately $23.07 if the loan is unsubsidized than if the loan was subsidized.

Jessica took out a Stafford loan worth $7,175 at the beginning of her six-year college career. The loan has a duration of ten years and an interest rate of 6.3%, compounded monthly. To calculate the monthly payments, we first need to determine the compound interest for both subsidized and unsubsidized scenarios.

For the unsubsidized loan: \[ P_{\text{unsubsidized}} = \frac{7175 \times (0.063/12) \times (1 + 0.063/12)^{10 \times 12}}{(1 + 0.063/12)^{10 \times 12} - 1} \]

And for the subsidized loan: \[ P_{\text{subsidized}} = \frac{7175 \times (0.063/12) \times (1 + 0.063/12)^{6 \times 12}}{(1 + 0.063/12)^{6 \times 12} - 1} \]

By calculating the monthly payments for both scenarios, we find that the payment for the unsubsidized loan is approximately $23.07 greater than the payment for the subsidized loan.

This difference is due to the accrued interest during Jessica's college career. Understanding the impact of interest rates and loan types on monthly payments is crucial for making informed financial decisions.