Question

Consider a 30-year, $155,000 mortgage with a rate of 6.05 percent. Ten years into the mortgage, rates have fallen to 5 percent. What would be the monthly saving to a homeowner from refinancing the outstanding mortgage balance at the lower rate?  (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

EMI as per old rates have to be calculated first

EMI = (P * R * (1 + R)^N) / (( 1 + R)^N -1)

R = 6.05% /12 = 0.5041% , N = 30 * 12 = 360

= ( 155000 * 6.05%/12 * (1+6.05%/12)^360) / ((1+ 6.05%/12)^360 - 1)

= 934.29

Now we need to calculate the balance outstanding after 10 years which could be seen in the amortisation schedule below

Month	Beginning amt	EMI	Interest	Principal	End Amount
1	1,55,000.00	934.29	781.46	152.83	1,54,847.17
2	1,54,847.17	934.29	780.69	153.60	1,54,693.57
3	1,54,693.57	934.29	779.91	154.38	1,54,539.19
4	1,54,539.19	934.29	779.14	155.15	1,54,384.03
5	1,54,384.03	934.29	778.35	155.94	1,54,228.10
6	1,54,228.10	934.29	777.57	156.72	1,54,071.37
7	1,54,071.37	934.29	776.78	157.51	1,53,913.86
8	1,53,913.86	934.29	775.98	158.31	1,53,755.55
100	1,35,441.14	934.29	682.85	251.44	1,35,189.70
101	1,35,189.70	934.29	681.58	252.71	1,34,936.99
102	1,34,936.99	934.29	680.31	253.98	1,34,683.01
103	1,34,683.01	934.29	679.03	255.26	1,34,427.74
104	1,34,427.74	934.29	677.74	256.55	1,34,171.19
105	1,34,171.19	934.29	676.45	257.84	1,33,913.35
106	1,33,913.35	934.29	675.15	259.14	1,33,654.20
107	1,33,654.20	934.29	673.84	260.45	1,33,393.75
108	1,33,393.75	934.29	672.53	261.76	1,33,131.99
109	1,33,131.99	934.29	671.21	263.08	1,32,868.91
110	1,32,868.91	934.29	669.88	264.41	1,32,604.50
111	1,32,604.50	934.29	668.55	265.74	1,32,338.76
112	1,32,338.76	934.29	667.21	267.08	1,32,071.68
113	1,32,071.68	934.29	665.86	268.43	1,31,803.25
114	1,31,803.25	934.29	664.51	269.78	1,31,533.46
115	1,31,533.46	934.29	663.15	271.14	1,31,262.32
116	1,31,262.32	934.29	661.78	272.51	1,30,989.81
117	1,30,989.81	934.29	660.41	273.88	1,30,715.93
118	1,30,715.93	934.29	659.03	275.26	1,30,440.67
119	1,30,440.67	934.29	657.64	276.65	1,30,164.01
120	1,30,164.01	934.29	656.24	278.05	1,29,885.97

Amount outstanding after 10 years = 129886 so now I = 5% (yearly) and N = 20 years * 12 = 240 months

EMI now = ( 129886 * 5%/12 * (1+5%/12)^240) / ((1+ 5%/12)^240 - 1) = 857.19

Monthly household saving = 934.29 - 857.19 = 77.10