Seven years go, Jean took out a 20- year 30000 loan at 8% effective on which she

Question

Seven years go, Jean took out a 20- year 30000 loan at 8% effective on which she was making annual payments, with the first payment due one year after the loan was taken out. She now wishes to make a lump-sum payment of 6000, and then pay off the loan in 5 more years. Find the revised annual payment under each of the following situations:

a) the lender is satisfied with earning 8% effective.

b) the lender is satisfied with 8% effective for the past 7 years, but insists on an 11% yield for the next 5 years.

c) the lender insists on an 11% yield for the entire life of the loan.

Explanation / Answer

Year Installment Interest Principal repaid Balance Principal                                                   1.0         3,055.6 2,400.00           655.60     29,344.40                                                   2.0         3,055.6 2,347.55           708.05     28,636.35                                                   3.0         3,055.6 2,290.91           764.69     27,871.66                                                   5.0         3,055.6 2,229.73           825.87     27,045.79                                                   6.0         3,055.6 2,163.66           891.94     26,153.86                                                   7.0         3,055.6 2,092.31           963.29     25,190.56 So Balance Principal after 7 years =      25,190.6 Less lump sum payment         6,000.0 Balance principal      19,190.6 a Assume the Installemnt A A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ Given A = periodical installment ? P=Loan amount = 19,190.6 i= interest rate per period = 8% pa n=total no of payments 5 years A= 0.08*19190.6*1.08^5/(1.08^5-1) A =4806.40 So Annual Installment = $ 4,806.40 b Assume the Installemnt A A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ Given A = periodical installment ? P=Loan amount = 19,190.6 i= interest rate per period = 11% pa n=total no of payments 5 years A= 0.11*19190.6*1.11^5/(1.11^5-1) A =5192.40 So Annual Installment = $ 5,192.40 c When the required yield 11% from beginning Year Installment Interest Principal repaid Balance Principal                                                   1.0         3,055.6 3,300.00         (244.40)     30,244.40                                                   2.0         3,055.6 3,326.88         (271.28)     30,515.68                                                   3.0         3,055.6 3,356.73         (301.13)     30,816.81                                                   5.0         3,055.6 3,389.85         (334.25)     31,151.06                                                   6.0         3,055.6 3,426.62         (371.02)     31,522.07                                                   7.0         3,055.6 3,467.43         (411.83)     31,933.90 So Balance Principal after 7 years =      31,933.9 Less lump sum payment         6,000.0 Balance principal      25,933.9 Assume the Installemnt A A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ Given A = periodical installment ? P=Loan amount = 25,933.9 i= interest rate per period = 11% pa n=total no of payments 5 years A= 0.11*25933.9*1.11^5/(1.11^5-1) A =7016.9 So Annual Installment = $ 7,016.90

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