Question

Part II-Mortgage Refinance Suppose your friend April is considering to refinance her mortgage. She bought her bonge 60 months ago. The amount of loan equals 154,000. 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 wear conventional loan with out-of-pocket closing costs of $3,000; c) 3.25% 30 vear 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

Value of the loan is 154000, rate is 5.25% and tenure is 30 years.

a) Hence current monthly EMI = pmt(5.25%/12,30*12,-154000) = 850.39

b) Amort Schedule:

Sr No	Current Principal	Principal	Interest	EMI	Closing Principal
1	154000	176.6437	673.75	850.3937	153823.3563
2	153823.3563	177.4165	672.9772	850.3937	153645.9398
3	153645.9398	178.1927	672.201	850.3937	153467.7471
4	153467.7471	178.9723	671.4214	850.3937	153288.7748
5	153288.7748	179.7553	670.6384	850.3937	153109.0194
6	153109.0194	180.5417	669.852	850.3937	152928.4777
7	152928.4777	181.3316	669.0621	850.3937	152747.1461
8	152747.1461	182.1249	668.2688	850.3937	152565.0212
9	152565.0212	182.9217	667.472	850.3937	152382.0994
10	152382.0994	183.722	666.6717	850.3937	152198.3774
11	152198.3774	184.5258	665.8679	850.3937	152013.8516
12	152013.8516	185.3331	665.0606	850.3937	151828.5185
13	151828.5185	186.1439	664.2498	850.3937	151642.3746
14	151642.3746	186.9583	663.4354	850.3937	151455.4163
15	151455.4163	187.7763	662.6174	850.3937	151267.64
16	151267.64	188.5978	661.7959	850.3937	151079.0422
17	151079.0422	189.4229	660.9708	850.3937	150889.6193
18	150889.6193	190.2516	660.1421	850.3937	150699.3677
19	150699.3677	191.084	659.3097	850.3937	150508.2838
20	150508.2838	191.92	658.4737	850.3937	150316.3638
21	150316.3638	192.7596	657.6341	850.3937	150123.6042
22	150123.6042	193.6029	656.7908	850.3937	149930.0013
23	149930.0013	194.4499	655.9438	850.3937	149735.5513
24	149735.5513	195.3007	655.093	850.3937	149540.2506
25	149540.2506	196.1551	654.2386	850.3937	149344.0955
26	149344.0955	197.0133	653.3804	850.3937	149147.0823
27	149147.0823	197.8752	652.5185	850.3937	148949.207
28	148949.207	198.7409	651.6528	850.3937	148750.4661
29	148750.4661	199.6104	650.7833	850.3937	148550.8557
30	148550.8557	200.4837	649.91	850.3937	148350.372
31	148350.372	201.3608	649.0329	850.3937	148149.0112
32	148149.0112	202.2418	648.1519	850.3937	147946.7694
33	147946.7694	203.1266	647.2671	850.3937	147743.6428
34	147743.6428	204.0153	646.3784	850.3937	147539.6275
35	147539.6275	204.9078	645.4859	850.3937	147334.7197
36	147334.7197	205.8043	644.5894	850.3937	147128.9154
37	147128.9154	206.7047	643.689	850.3937	146922.2107
38	146922.2107	207.609	642.7847	850.3937	146714.6017
39	146714.6017	208.5173	641.8764	850.3937	146506.0844
40	146506.0844	209.4296	640.9641	850.3937	146296.6548
41	146296.6548	210.3458	640.0479	850.3937	146086.3089
42	146086.3089	211.2661	639.1276	850.3937	145875.0428
43	145875.0428	212.1904	638.2033	850.3937	145662.8525
44	145662.8525	213.1187	637.275	850.3937	145449.7337
45	145449.7337	214.0511	636.3426	850.3937	145235.6826
46	145235.6826	214.9876	635.4061	850.3937	145020.695
47	145020.695	215.9282	634.4655	850.3937	144804.7669
48	144804.7669	216.8728	633.5209	850.3937	144587.894
49	144587.894	217.8217	632.572	850.3937	144370.0724
50	144370.0724	218.7746	631.6191	850.3937	144151.2977
51	144151.2977	219.7318	630.6619	850.3937	143931.566
52	143931.566	220.6931	629.7006	850.3937	143710.8729
53	143710.8729	221.6586	628.7351	850.3937	143489.2142
54	143489.2142	222.6284	627.7653	850.3937	143266.5858
55	143266.5858	223.6024	626.7913	850.3937	143042.9834
56	143042.9834	224.5806	625.8131	850.3937	142818.4028
57	142818.4028	225.5632	624.8305	850.3937	142592.8396
58	142592.8396	226.55	623.8437	850.3937	142366.2896
59	142366.2896	227.5412	622.8525	850.3937	142138.7484
60	142138.7484	228.5367	621.857	850.3937	141910.211

Principal paid in 60 installments : 12089.78

Interest Paid in 60 installments : 38933.83

c) Amount to be refinanced (It is the balance principal after 60 installments) : 141910.211