Question

A student is graduating from college in 12 months but will need a loan in the amount of $10,720 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are: Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $11,443.63 at graduation Which loan will have a lower balance, and by how much, at the time of repayment?

Answer 1

The Unsubsidized Stafford Loan will have a lower balance of $10,783.99 compared to the PLUS Loan's balance of $11,517.76 at the time of repayment.

Step-by-step explanation:

Loan Comparison:

• Unsubsidized Stafford Loan: Annual interest rate of 5.95%, compounded monthly, with a payment grace period of six months from time of graduation.
• PLUS Loan: Annual interest rate of 6.55%, compounded monthly, with a balance of $11,443.63 at graduation.

To determine which loan will have a lower balance at the time of repayment, we need to compare the total amount accrued by each loan over 12 months. First, let's calculate the balance of the Unsubsidized Stafford Loan after 12 months:

Balance = Principal + Interest

Interest = Principal x Rate x Time

Principal = $10,720
Rate = 5.95% / 12 = 0.4958% (monthly rate)
Time = 12 months

Interest = $10,720 x 0.4958% x 12 = $63.99

Balance = $10,720 + $63.99 = $10,783.99

Now, let's calculate the balance of the PLUS Loan after 12 months:

Principal = $11,443.63
Rate = 6.55% / 12 = 0.5458% (monthly rate)

Interest = $11,443.63 x 0.5458% x 12 = $74.13

Balance = $11,443.63 + $74.13 = $11,517.76

Therefore, the Unsubsidized Stafford Loan will have a lower balance of $10,783.99 compared to the PLUS Loan's balance of $11,517.76 at the time of repayment.