Question

Suppose your friend April is considering to refinance her mortgage. She bought her house 60 months ago. The amount of loan equals 154,00. She paid cash to cover the 5% down payment plus all required closing costs (closing costs include application fee, appraisal fee, loan origination fees and other costs, usually about 3%-5% of the loan amount). Since she had a decent credit history and relatively stable income, her mortgage rate was 5.25% for 30 years at the time of the purchase. Since her down payment was less than 20%, she had to pay monthly mortgage insurance premium which is $80 per month (premiums are automatically terminated when the LTV ratio (loan-to-value ratio) falls below 80%). Recently, mortgage rate has been dropping and she is considering to refinance her mortgage. She talked with a mortgage banker and got the following information: a) 3.75% 30 year conventional loan with out-of-pocket closing costs of $1,800; b) 3.5% 30 year conventional loan with out-of-pocket closing costs of $3,000; c) 3.25% 30 year conventional loan with out-of-pocket closing costs of $4,000. Based on the recent appraisal, her house value has changed to $180.000. Please advise her on the following: 1) Based on the information, please calculate her monthly mortgage payment on the original loan. Please show your process. 2) Please use online resources to show her amortization table (please only print out her first 60 payments on the amortization table). How much principle has she paid off so far? How much interest has she paid over the past 60 payments? 3) How much does she need to refinance now? Hint: You need to find her loan balance. 4) Based on the new appraisal value, what is her LTV (loan-to-value) ratio now? 5) Does she still need to pay the mortgage insurance premium after refinancing? Why? 6) How much should her monthly payment be under each option (a, b, and c)? Show your calculations. 7) Would you suggest her to do the refinancing or not? Why? Notice that monthly payment is reduced but she need to make 360 payments plus closing costs under the new mortgage versus 300 payments in the old mortgage. 8) Which option would you suggest her to take? What factors would affect her choice and how?

Answer 1

1) Calculation of monthly mortgage payment on the original loan :-

[PXRX (1+R)"] [ (1+ R)"11 Monthly mortgage payment where, Principal Amount of Loan Rate of Interest per month P R No. of monthly instalments N In the present case, P 15400 R 0.4375 % (i.e. 5.25%/12) (i.e. 30 Years X 12 Months) N 360 Therefore, (15400 X (0.0525/12) X (1+(0.0525/12) )360 (1+(0.0525/12))360-1 Monthly mortgage payment 324.36 3.81 85.04 Thus, monthly mortgage payment on the original loan of April is 85.04

2) Amortisation Table :-

Total Monthly Sr. No. of Opening Interest for the Principal Repaid Closing Outstanding of month @ 5.25 % Instalment Outstanding of Mortgage Mortgage Loan Payment Payment Mortgage Loan p.a (A) (B) (C) (D) (B) 5.25% /12 (E) (C)-(D) (F) (B)-(E) 67.38 15,400.00 85.04 17.66 15,382.34 15,382.34 85.04 2 67.30 17.74 15,364.59 15,346.77 15,364.59 85.04 67.22 17.82 85.04 4 15,346.77 67.14 17.90 15,328.88 85.04 67.06 5 15,328.88 17.98 15,310.90 15,310.90 6 85.04 66.99 18.05 15,292.85 85.04 7 15,292.85 66.91 18.13 15,274.71 8 15,274.71 85.04 66.83 18.21 15,256.50 15,256.50 85.04 66.75 18.29 15,238.21 10 15,238.21 85.04 66.67 18.37 15,219.84 85.04 11 15,219.84 66.59 18.45 15,201.39 85.04 66.51 18.53 12 15,201.39 15,182.85 13 15,182.85 85.04 66.42 18.61 15,164.24 14 15,164.24 85.04 66.34 18.70 15,145.54 85.04 15,126.76 15 15,145.54 66.26 18.78 85.04 66.18 16 15,126.76 18.86 15,107.90 15,107.90 17 85.04 66.10 18.94 15,088.96 15,088.96 19.03 18 85.04 66.01 15,069.94

15,069.94 19 85.04 65.93 19.11 15,050.83 19.19 20 15,050.83 85.04 65.85 15,031.64 85.04 21 15,031.64 65.76 19.28 15,012.36 15,012.36 85.04 19.36 22 65.68 14,993.00 23 14,993.00 85.04 65.59 19.44 14,973.56 24 14,973.56 85.04 65.51 19.53 14,954.03 85.04 25 14,954.03 65.42 19.62 14,934.41 85.04 14,914.71 26 14,934.41 65.34 19.70 27 14,914.71 85.04 65.25 19.79 14,894.92 28. 14,894.92 85.04 65.17 19.87 14,875.05 85.04 19.96 29 14,875.05 65.08 14,855.09 14,855.09 85.04 64.99 20.05 14,835.04 30 64.90 31 14,835.04 85.04 20.14 14,814.90 85.04 20.22 32 14,814.90 64.82 14,794.68 14,794.68 85.04 64.73 33 20.31 14,774.36 14,774.36 34 85.04 64.64 20.40 14,753.96 35 14,753.96 85.04 64.55 20.49 14,733.47 85.04 36 14,733.47 64.46 20.58 14,712.89 64.37 37 14,712.89 85.04 20.67 14,692.22 38 14,692.22 85.04 64.28 20.76 14,671.46 39 14,671.46 85.04 64.19 20.85 14,650.61 85.04 40 14,650.61 64.10 20.94 14,629.67 85.04 21.03 14,608.63 41 14,629.67 64.00 42 14,608.63 63.91 14,587.50 85.04 21.13 14,587.50 63.82 14,566.29 43 85.04 21.22

44 14,566.29 85.04 63.73 21.31 14,544.97 14,523.57 45 14,544.97 85.04 63.63 21.41 46 14,523.57 85.04 63.54 21.50 14,502.07 47 14,502.07 85.04 63.45 21.59 14,480.48 63.35 48 14,480.48 85.04 21.69 14,458.79 63.26 49 14,458.79 85.04 21.78 14,437.01 63.16 21.88 50 14,437.01 85.04 14,415.13 21.97 51 14,415.13 85.04 63.07 14,393.16 52 14,393.16 85.04 62.97 22.07 14,371.09 22.17 53 14,371.09 85.04 62.87 14,348.92 22.26 14,326.66 54 14,348.92 85.04 62.78 85.04 62.68 55 14,326.66 22.36 14,304.30 56 14,304.30 85.04 62.58 22.46 14,281.84 14,281.84 14,259.28 57 85.04 62.48 22.56 58 14,259.28 85.04 62.38 22.66 14,236.63 62.29 59 14,236.63 85.04 22.75 14,213.87 60 14,213.87 85.04 62.19 22.85 14,191.02 Total 5,102.36 3,893.38 1,208.98

Thus,

Principal paid so far by April = 1208.98

Interest paid over past 60 payments = 3893.38

3) The amount of refinance :-

April needs to refinance 14191.02 now, which is equal to present balance outstanding on the original loan.