Short Answer 
The loan details for both subsidized and unsubsidized Stafford Loans include amounts of $7,855, with interest rates of 3.7% and 4.7%, respectively, over 18 months. After calculations, the future values are $8,180.62 for the unsubsidized loan and $8,262.19 for the subsidized loan, resulting in a difference of $81.57. This difference suggests a potential error or misunderstanding in calculations or options provided.
Step 1: Understand the Loan Details
Begin by identifying the loan specifics for both the unsubsidized and subsidized Stafford Loans. You need to note the following:
- Loan Amount: $7,855
- Unsubsidized Interest Rate: 3.7% per year
- Subsidized Interest Rate: 4.7% per year
- Loan Duration: 18 months (or 1.5 years)
Step 2: Calculate the Future Value of Each Loan
Utilize the formula for compound interest to calculate the future values of both loans. For each loan, apply the formula A = P(1 + r/n)^(nt), where:
- A = future value
- P = principal amount ($7,855)
- r = annual interest rate (as decimal)
- n = number of compounding periods per year (12 for monthly)
- t = time in years (1.5 for 18 months)
Calculate for:
- Unsubsidized Loan Future Value = $8,180.62
- Subsidized Loan Future Value = $8,262.19
Step 3: Determine the Difference in Loan Balances
Finally, find the difference between the future values of both loans at graduation. Subtract the future value of the unsubsidized loan from the subsidized loan:
- Difference = $8,262.19 – $8,180.62 = $81.57
This indicates a discrepancy, as the calculated difference does not match any options provided, prompting a review of calculation methods or understanding of the scenario.