Question

Michael is graduating from college in one year and needs a loan of $9,056 for his last two semesters. He may either receive an unsubsidized Stafford loan with an interest rate of 6.8% compounded monthly or his parents may obtain a PLUS loan with an interest rate of 7.8% compounded monthly. The Stafford loan has a grace period of six months from the time of graduation. Which loan will have a higher balance at the time of repayment and by how much?

A) The PLUS loan has a higher balance by $94.67
B) The PLUS loan has a higher balance by $150.59
C) The PLUS loan has a higher balance by $237.40
D) The PLUS loan has a higher balance by $334.21

Answer 1

The PLUS loan will have a higher balance at the time of repayment by $237.40.

Step-by-step explanation:

To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of each loan. For the unsubsidized Stafford loan, the principal is $9,056, the interest rate is 6.8% compounded monthly, and the loan term is 6 months grace period + 12 months of repayment = 18 months. For the PLUS loan, the principal is the same, but the interest rate is 7.8% compounded monthly, and the loan term is 12 months of repayment. Using the future value formula:

Future Value = Principal * (1 + Interest Rate/12)^Number of Months

For the unsubsidized Stafford loan:

Future Value = $9,056 * (1 + 0.068/12)^(18)

For the PLUS loan:

Future Value = $9,056 * (1 + 0.078/12)^(12)

Calculating these values gives:

For the unsubsidized Stafford loan: $9,056 * (1 + 0.068/12)^(18) = $9,150.59

For the PLUS loan: $9,056 * (1 + 0.078/12)^(12) = $9,237.40

Therefore, the PLUS loan will have a higher balance at the time of repayment, by $237.40.