A homeowner has $200,000 home with a 20-year mortgage, paid monthly at a quoted

Question

A homeowner has $200,000 home with a 20-year mortgage, paid monthly at a quoted interest rate of 7.25% per year compounded semi-annually. After five years he receives $50,000 as an inheritance. If he pays this $50,000 toward his mortgage along with his regular payment, by approximately how many years will it reduce the amount of time it takes him to pay off his mortgage? Five years ago you took out a 30-year mortgage with a quoted interest rate of 6.5% per year compounded semi-annually for $200,000. If you were to refinance the mortgage today for 20 years at a quoted rate of 4.25% per year compounded semi-annually, how much would you save in total interest expense?

Explanation / Answer

Annual installment for a mortgage loan A = P x r(r+1)^n/[(r+1)^n-1] Where P = Mortgage loan amount = 200,000 r = rate of interest = 7.25%/200 = 0.03625 n = no of period = 20year x 2 = 40 therefore A = 200,000 x 0.03625 x 1.03625^40/(1.03625^40-1) Or, A = 200,000 x 0.150622/3.155103 Or, A = 9547.865 His Payment Schedule are as follows: Beginning Ending Period Balance Interest Principal Balance 1 200000 7250 2297.87 197702.1 2 197702.1 7166.702 2381.168 195321 3 195321 7080.385 2467.485 192853.5 4 192853.5 6990.939 2556.931 190296.5 5 190296.5 6898.25 2649.62 187646.9 6 187646.9 6802.201 2745.669 184901.3 7 184901.3 6702.671 2845.199 182056.1 8 182056.1 6599.532 2948.338 179107.7 9 179107.7 6492.655 3055.215 176052.5 10 176052.5 6381.903 53165.97 122886.5 Paid at the end of 5 year $50,000 in addition of installment 11 122886.5 4454.637 5093.233 117793.3 12 117793.3 4270.007 5277.863 112515.4 13 112515.4 4078.685 5469.185 107046.3 14 107046.3 3880.427 5667.443 101378.8 15 101378.8 3674.982 5872.888 95505.92 16 95505.92 3462.09 6085.78 89420.14 17 89420.14 3241.48 6306.39 83113.75 18 83113.75 3012.874 6534.996 76578.76 19 76578.76 2775.98 6771.89 69806.87 20 69806.87 2530.499 7017.371 62789.5 21 62789.5 2276.119 7271.751 55517.75 22 55517.75 2012.518 7535.352 47982.4 23 47982.4 1739.362 7808.508 40173.89 24 40173.89 1456.303 8091.567 32082.32 25 32082.32 1162.984 8384.886 23697.43 26 23697.43 859.032 8688.838 15008.6 27 15008.6 544.0616 9003.808 6004.788 28 6004.788 217.6736 6004.788 0 So in changed situation he will be able to pay loan in 28/2 = 14 year Hence he will be able to reduce 20 years - 14 years = 6 year Answer:6 year

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