Question

Betty just purchased a home. She took out a mortgage of $600,000 amortized over 30 years at a rate of j2=4% with monthly payments. After 4 years, she refinanced her mortgage at a rate of j2=3.8% for the remaining 26 years. Calculate her new monthly payment after refinancing. Round all of your loan payments up to the next cent. On your worksheet, clearly label and show your work for each step (formulas or calculator inputs). Your Answer: Answer

Answer 1

First of all we will calculate the monthly payments

N = Total Month = 30*12 = 360

I/Y = Monthly Interest Rate = 4/12 = 0.33 %

PV = -600000

CPT PMT = 2864.477

Or ie can be calculated as under

EMI = 600000 / PVAF 360 , 0.33

EMI = 600000 / 209.4622522 = 2864.477

NOw we will calculate outstanding after 4 years

Month	Opeing Balance	Interest @ 0.33%	EMI	Cl Bal
1	600000	1980	2864.5	599115.52
2	599,116	1,977	2,864	598,228
3	598,228	1,974	2,864	597,338
4	597,338	1,971	2,864	596,445
5	596,445	1,968	2,864	595,548
6	595,548	1,965	2,864	594,649
7	594,649	1,962	2,864	593,747
8	593,747	1,959	2,864	592,842
9	592,842	1,956	2,864	591,934
10	591,934	1,953	2,864	591,023
11	591,023	1,950	2,864	590,109
12	590,109	1,947	2,864	589,191
13	589,191	1,944	2,864	588,271
14	588,271	1,941	2,864	587,348
15	587,348	1,938	2,864	586,422
16	586,422	1,935	2,864	585,493
17	585,493	1,932	2,864	584,560
18	584,560	1,929	2,864	583,625
19	583,625	1,926	2,864	582,686
20	582,686	1,923	2,864	581,745
21	581,745	1,920	2,864	580,800
22	580,800	1,917	2,864	579,852
23	579,852	1,914	2,864	578,901
24	578,901	1,910	2,864	577,947
25	577,947	1,907	2,864	576,990
26	576,990	1,904	2,864	576,029
27	576,029	1,901	2,864	575,066
28	575,066	1,898	2,864	574,099
29	574,099	1,895	2,864	573,129
30	573,129	1,891	2,864	572,156
31	572,156	1,888	2,864	571,180
32	571,180	1,885	2,864	570,200
33	570,200	1,882	2,864	569,217
34	569,217	1,878	2,864	568,231
35	568,231	1,875	2,864	567,242
36	567,242	1,872	2,864	566,249
37	566,249	1,869	2,864	565,253
38	565,253	1,865	2,864	564,254
39	564,254	1,862	2,864	563,252
40	563,252	1,859	2,864	562,246
41	562,246	1,855	2,864	561,237
42	561,237	1,852	2,864	560,225
43	560,225	1,849	2,864	559,209
44	559,209	1,845	2,864	558,190
45	558,190	1,842	2,864	557,167
46	557,167	1,839	2,864	556,142
47	556,142	1,835	2,864	555,112
48	555,112	1,832	2,864	554,080

Closing Balance of loan after 4 years = 554,080

Claculation of New monthly payments=

PV = -554080

I/Y = 3.8/12 = 0.3166

N = 26*12 = 312

CPT PMT = 2760.96

or

EMI = 554080 / PVAF 312 , 0.3166%

EMI = 554080 / 198.030 = 2760.96