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?

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