Answer:
To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.
The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.
The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:
Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)
Plugging in the given values, we have:
Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16
The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.
The balance of the PLUS loan at the time of repayment can be calculated using the same formula:
Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54
Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.
Explanation: