UECM 1403 Theory of Interest A loan ors 1,000 is being repaid at 8% effective by

Question

UECM 1403 Theory of Interest A loan ors 1,000 is being repaid at 8% effective by level annual payments of S125, what is the outstanding balance just after the 8 payment? 5. (3 marks) Bert has a $100,000 25-year mortgage with a 12% nominal interest rate convertible monthly. The first payment is due one month after the mortgage is taken out. Twelve years after taking out the mortgage (ater making his 144h payment), he refinances with a new nominal interest of 896, also convertible monthly. The new mortgage will be paid off on the same date as the original one. Calculate the difference in monthly mortgage payment after refinancing. (7 marks)

Explanation / Answer

1) The outstanding balance after the 8th payment can be found out by preparing a loan amortization schedule as below: Year Beginning balance Interest for the year Total loan balance Installment paid Ending loan balance 1 1000.00 80.00 1080.00 125.00 955.00 2 955.00 76.40 1031.40 125.00 906.40 3 906.40 72.51 978.91 125.00 853.91 4 853.91 68.31 922.22 125.00 797.22 5 797.22 63.78 861.00 125.00 736.00 6 736.00 58.88 794.88 125.00 669.88 7 669.88 53.59 723.47 125.00 598.47 8 598.47 47.88 646.35 125.00 521.35 Loan oustanding after the 8th payment = $521.35. 6) The annual installments on the original loan = 100000*0.01*1.01^300/(1.01^300-1) = $     1,053.22 The loan outstanding after the 144th payment is the PV of the remaining 156 installments, which is equal to = 1053.22*(1.01^156-1)/(0.01*1.01^156) = $   83,017.90 The annual installments on the refinanced loan = 83017.90*0.01*1.01^300/(1.01^300-1) = $         874.36 Difference in monthly mortgage payments after refinancing = 1053.22-874.36 = $         178.86

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