Gilbert is graduating from college in one year, but he will need a loan in the amount of $5,125 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 get 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?

Question

03-11-2017
Mathematics

contestada

Gilbert is graduating from college in one year, but he will need a loan in the amount of $5,125 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 get 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?

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Yna9141 Yna9141 · Answer 1 · 2017-11-14T14:03:08+01:00

First, determine the effective interests given both interest rates.

(1) ieff = (1 + 0.068/12)^12 - 1 = 0.07016
(2) ieff = (1 + 0.078/12)^12 - 1 = 0.08085

Calculating the interests will entail us to use the equation,
I = P ((1 + i)^n - 1)

Substituting the known values,
(1) I = ($5125)((1 + 0.07016)^1/2 - 1)
I = $176.737

(2) I = ($5125)(1 + 0.08085)^1/2 - 1)
I = $203.15

a. Hence, the greater interest will be that of the second loan.

b. The difference between the interests,
d = $203.15 - $176.737
$26.413