Question

Consider Gavin, a new freshman who has just received a Stafford student loan and started college. He plans to obtain the maximum loan from Stafford at the beginning of each year. Although Gavin does not have to make any payments while he is in school, the unsubsidized 6.8 percent interest owed (compounded monthly) accrues and is added to the balance of the loan. UNSUBSIDIZED Stafford loan limits: Freshman $6,000 Sophomore 6,000 Junior 7,000 Senior 7,000 After graduation, Gavin gets a 6-month grace period. This means that monthly payments are still not required, but interest is still accruing. After the grace period, the standard repayment plan is to amortize the debt using monthly payments for ten years. a. Show a time line of when the loans will be taken. b. What will be the loan balance when Gavin graduates after his fourth year of school? c. What is the loan balance six months after graduation? d. Using the standard repayment plan and a 6.8 percent APR interest rate, compute the monthly payments Gavin owes after the grace period.

Answer 1

	a	Future Value(FV) of cash flowat end of 48 months:
		(Cash Flow)* ((1+i)^(48-N))
		i= monthly interest rate=(6.8/12)%=0.566667%	0.00566667
		N=Year of Cash Flow
		N	A	B=A*(1.00566667^(48-N)
		Month End	Loan amount	FV after 48 months
		0	$6,000	7869.47901
		12	$6,000	7353.554214
		24	$7,000	8016.695823
		36	$7,000	7491.11946
		48	Graduation	30730.84851	SUM
		54	End of grace period
	b	LOAN BALANCE WHEN GAVIN GRADUATES	$     30,730.85
	c	LOAN BALANCE SIX MONTHS AFTER GRADUATION	$     31,790.61	(30730.85*(1.00566667^6)
		Number of months of monthly payment	120	(12*10)
		Monthly Payment (Assuming beginning of month payment)	$363.79	(Using PMT function of excel with Rate=(6.8/12)%,Nper=120,PV=-31790.61, Type=1)