Emmett is graduating from college in six months, but he will need a loan in the amount of $2,350 for his last semester. 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 and by how much at the time of repayment?

Question

anonymous · Answer

A. The PLUS Loan has a higher balance by $25.12
B. The Stafford Loan has a higher balance by $71.73
C. The PLUS Loan has a higher balance by $125.80
D. The Stafford Loan has a higher balance by $158.45

aum · Answer

Here is the compound interest formula: $$\Large A = P(1 + \frac{ r }{ n })^{nt}$$A = Amount at maturity
P = Principal Amount = $2,350
r = Annual interest rate in decimal = 0.068 (Stafford loan)  or  0.078 (PLUS loan)
n = compounding period (compounded how many times a year) = 12
t = years invested = 0.5 years

Use the above formula and compute A for both loans and take the difference.