e. While Edward was a student at Orange University, he borrowed $12,000 in stude
ID: 2668246 • Letter: E
Question
e. While Edward was a student at Orange University, he borrowed $12,000 in student loan at an annual interest rate of 9%. If he repays $1,500 pear year, calculate the period required (to the nearest year) to pay off his debt.f. Peter receives a payment of $100,000 from his grandmother’s estate. The entire amount is invested at a rate of interest of 10% and he expects to receive 150 equal monthly payments. The first payment is expected in 2 years. Find the size of the payments.
g. An investment firm X pays 10% interest per annum, compounded on a quarterly basis. To remain competitive, the investment manager of another firm (firm Y) is willing to match the interest rate offered by firm X, but interest will be compounded on a monthly basis. What nominal rate of interest must firm Y offer to its clients?
Explanation / Answer
e. Principal = $12000, Rate = 9%, PMT =$1500 we need to find Time for repayment = nper We have nper function in excel which gives Period = nper(Rate,PMT,PV) ie Period = nper(9%,1500,-12000) = 14.77 years ie 15 Yrs. So it will take 15 Yrs to repay the Loan f. In 2 Yrs, the Initial amt of $100,000 will grow at compunded rate of 10%pa to = 100000*(1+10%)^2 = $121,000 = PV This amount (PV) will be repaid to him in nper = 150 Inst at Rate = 10% annual pr 10%/12 monthly We need to find PMT ie each payment We have excel function PMT = PMT(Rate,nper,PV) = Rate(10%/12,150,-121000) = $1,416.18 So size of the payment is $1416.18 per month g. Effective Int Rate EIR r = (1+i/n)^n - 1 where i is nominal Int rate & n is no of compunding in a year In case of X, we have i=10%, n = 12month/3month = 4 SO EIRx = (1+10%/4)^4-1 = 10.38% For Y, n = 12month/12month = 1, EIRy=EIRx=10.38%, we need to find i=? So we have EIR = (1+i/n)^n -1 putting n=1 we get EIR = (1+i/1)^1 -1 = 1+i-1 = i = 10.38% So Nominal rate to Y client will be 10.38% per annum wih monthly compounding. Thus to a uninformed customer, Y's rate will look more attractive than X's.
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