A student has the Stafford deferred interest loan with 6.8% interest compounded
ID: 2649261 • Letter: A
Question
A student has the Stafford deferred interest loan with 6.8% interest compounded monthly. Although the payment on the loan payment is deferred, the interest accrues every month. The total loan will need to be repaid six months after graduation. The payment will be monthly for the next 10 years. The student will borrow (see below) at the beginning of each year and does not plan to make any payment on the loan until six months after graduation. (Use fin calculator, format 2nd P/Y=12 enter, 2nd BGN 2nd enter 2nd CPT for beginning cash flows)
Loan amount Future Value
Year 1 $10,000
Year 2 $13,000
Year 3 $14,000
Year 4 $15,000
Calculate how much will the total loan including interest on graduation at the end of year 4 ($61,134)._______________
Calculate the loan balance at the end of six months after graduation._________________
When the student starts paying for the loan, how much will the end of the month loan payment be? _____________
Explanation / Answer
Calculate how much will the total loan including interest on graduation at the end of year 4
Total loan including interest on graduation at the end of year 4 = fv(rate,nper,pmt,pv) + fv(rate,nper,pmt,pv) + fv(rate,nper,pmt,pv) + fv(rate,nper,pmt,pv)
Total loan including interest on graduation at the end of year 4 = fv(6.8%/12,12*4,0,-10000) + fv(6.8%/12,12*3,0,-13000) + fv(6.8%/12,12*2,0,-14000) + fv(6.8%/12,12*1,0,-15000)
Total loan including interest on graduation at the end of year 4 = $ 61,134.28
Alternatively
Total loan including interest on graduation at the end of year 4 = 10000 * (1+ 6.8%/12)^(12*4) + 13000 * (1+ 6.8%/12)^(12*3) + 14000 * (1+ 6.8%/12)^(12*2) + 15000 * (1+ 6.8%/12)^(12*1)
Total loan including interest on graduation at the end of year 4 = $ 61,134.28
Calculate the loan balance at the end of six months after graduation._________________
Loan balance at the end of six months after graduation = fv(rate,nper,pmt,pv)
Loan balance at the end of six months after graduation = fv(6.8%/12,6,0,-61134.28)
Loan balance at the end of six months after graduation = $ 63,242.52
Alternatively
Loan balance at the end of six months after graduation = 61134.28 * (1+ 6.8%/12)^(6)
Loan balance at the end of six months after graduation = $ 63,242.52
When the student starts paying for the loan, how much will the end of the month loan payment be? _____________
Monthly Payment = pmt(rate,nper,pv,fv)
rate = 6.8%/12
nper = 10Years * 12 = 120 Month
pv (loan balance at the end of six months) = 63,242.52
Fv = 0
Monthly Payment = pmt(6.8%/12,120,-63242.52,0)
Monthly Payment = $ 727.80
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