Mark is graduating from college in six months, but he will need a loan in the amount of $7,038 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 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?

Question

tkhunny · Answer

There are a couple of oddities, here.

1) Is it clear that the Stafford does or does not accrue interest during the Grace Period?
2) The PLUS loan is due for repayment immediately upon final disbursement.  There is no waiting for graduation and there is no interest accumulation.

Thus, if interest is accrued during the grace period, the Stafford is the obvious choice.  If no such accrual occurs, it's a tie.

anonymous · Answer

thanks! can you help me find the right equation for this? Naomi uses a credit card with a 25.9% APR, compounded monthly, to pay for a hotel stay totaling $971.20. She can pay $400 per month on the card. What will the total cost of this purchase be?

tkhunny · Answer

This is a walk-off.  No formula needed.

i = 0.259 -- Annual Interest
j = i/12 -- Monthly Interest
r = 1+j -- Monthly Accumulation Factor

971.20*r - 400 = 592.16
592.16*r - 400 = 204.94
204.94*r = 209.37

That's about it.