Final answer:
The Stafford Loan will have a lower balance by $70.47 at the time of repayment.
Step-by-step explanation:
The Stafford Loan will have a lower balance by $70.47 at the time of repayment.
To determine the final balance of each loan at the time of repayment, we need to calculate the accumulated amount. For the Unsubsidized Stafford Loan, we have an initial balance of $3,901.95 and an annual interest rate of 4.65%, compounded monthly. Since the loan will be repaid in 6 months, we need to calculate the accumulated amount for 6 months. Using the formula: A = P(1 + r/n)^(nt), where A is the accumulated amount, P is the principal balance, r is the annual interest rate, n is the number of times compounded per year, and t is the time in years, we can calculate the accumulated amount as follows:
A = $3,901.95(1 + 0.0465/12)^(12(6/12))
A = $3,901.95(1 + 0.003875)^(6)
A = $3,901.95(1.003875)^(6)
A = $3,901.95(1.02356562574)
A = $3,997.42045270355
The final balance of the Unsubsidized Stafford Loan at the time of repayment is $3,997.42.
For the PLUS Loan, we have an initial balance of $3,725 and an annual interest rate of 5.65%, compounded monthly. The loan will be repaid in 6 months, so we need to calculate the accumulated amount for 6 months. Using the same formula, we can calculate the accumulated amount as follows:
A = $3,725(1 + 0.0565/12)^(12(6/12))
A = $3,725(1 + 0.00470833333)^(6)
A = $3,725(1.00470833333)^(6)
A = $3,725(1.02869252637)
A = $3,829.07595252925
The final balance of the PLUS Loan at the time of repayment is $3,829.08.
Therefore, the Stafford Loan will have a lower balance by $70.47 at the time of repayment.