Question

A student is graduating from college in 12 months but will need a loan in the amount of $9,529 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 $10,172.23 at graduation

Which loan will have a lower balance, and by how much, at the time of repayment?

Answer 1

To compare the balances of the two loans at the time of repayment, we need to calculate the future value of the loan amount for each loan option after 12 months of compounding.

For the Unsubsidized Stafford Loan:

Principal (P) = $9,529

Annual interest rate (r) = 5.95%

Compounding period (n) = 12 (monthly compounding)

Time period (t) = 1 year

Using the formula for future value of a loan (FV), we get:

The formula is:

FV = P * (1 + r/n)^(nt) = $9,529 * (1 + 0.0595/12)^(121) = $10,087.14

For the PLUS Loan:

Principal (P) = $10,172.23

Annual interest rate (r) = 6.55%

Compounding period (n) = 12 (monthly compounding)

Time period (t) = 1 year

Using the same formula, we get:

FV = P * (1 + r/n)^(nt) = $10,172.23 * (1 + 0.0655/12)^(121) = $10,774.71

Therefore, the Unsubsidized Stafford Loan will have a lower balance at the time of repayment, by $687.57 ($10,087.14 - $10,774.71).