1.For a $240,000 loan with monthly payments, at 8% interest for 25 years, the bo
ID: 1171426 • Letter: 1
Question
1.For a $240,000 loan with monthly payments, at 8% interest for 25 years, the borrower had to pay 2 points in origination fees at the time the loan was made. If that loan is paid off in 5 years what is the effective yield of the loan, including the origination fees
2. (using info from question 2) Now presume that in addition to the points at the origination above, the borrower also has to pay 1 point in prepayment penalty at the time the loan is paid off. What is the EFFECTIVE yield including the origination fees and the prepayment penalty
Explanation / Answer
1) Calculation of Effective Yield (loan paid in 5 yrs.) Loan Made 240000 Origination Fees (2 Points i.e. 2% of Loan) 4800 Net Outflow 235200 Calculation Of Monthly Installement (Using Excel) PMT(R,Nper,Pv,Fv,0/1) R=Rate of Interest=(8%/12)=0.67% Nper=No of Periods=5*12=60 Pv =Amt set Aside Today=235200 Fv=Goal To Be Achived=0 0=For Investment at yr end=0 4773.51 Calculation Of Monthly Installement (Using Mathematics Formulas) Pv=Annual Installment * PVAF(R,N) (PVAF means Pv of Annuity Factor) Pv=235200 R = rate of Interest per Period=0.67% N=No of Periods=60 235200=AI*PVAF(1+0.67%)^60 AI=4773.51 Effective Yield: initial Outflow= Future Inflow Inflows PVAF @ 5%(i.e5/12=0.42%) PVAF @ 5.5% PVAF @ 7% PVAF @ 7.5% PVAF @ 7.95% PVAF @ 7.98% PVAF @ 7.99% 4773.5100 52.9393 52.3275 50.5016 49.9053 49.3767 49.3417 49.3277 252,706.28 249,785.84 241,069.89 238,223.45 235,700.17 235,533.10 235,466.27 Approx: 7.99% Effective Yield Reduced Due to Initial Point Payment 2) in continuation of Above : Effctive yield initial Outflow= Future Inflow(Installments + penalty at the end of 5 yrs) Prepayment Penalty (1 point) 2400 PVAF(8.2%p.a) PVAF(8.5%p.a) Inflows 4773.51 49.091 234,336.38 48.7416 232,668.52 2400 0.6647 1,595.28 0.6547 1,571.28 235,931.66 234,239.80 By Using Interpolation Tecnique: {(235931.66-235200)/235931.66-234239.80}*0.3% 0.13% Approx 8.33% (8.2+0.13)
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