Question

Explain why that plan is good for each person, including how much money they will save over the entire time of the loan and the amount of the new payments. Show the math. The original mortgage was 30 years at 7.5%, for 600,000. It was taken 4 years ago.

PERSON 1 - Refinance: change to 15 years at 6.8%

PERSON 2 - Refinance: For 30 years at 7.1%, reducing monthly payment.

PERSON 3 - Don't refinance.

Answer 1

The monthly payment on the original loan is calculated as follows

PMT = Present value of loan 1 - ( 1 + interest rate)^-nt ( interest rate)

PMT = $ 600,000 1 - ( 1 (0.075/12))^-12x30 ( 0.075/12)

PMT = $ 4,195.29

The amortization schedule on the original loan for 4 years is shown below

Month	Beginning balance	Monthly payment	Interest	Principal	Ending balance
1	$600,000	$4,195.29	$3,750	$445.29	$599,554.71
2	$599,554.71	$4,195.29	$3,747	$448.07	$599,106.64
3	$599,106.64	$4,195.29	$3,744	$450.87	$598,655.76
4	$598,655.76	$4,195.29	$3,742	$453.69	$598,202.07
5	$598,202.07	$4,195.29	$3,739	$456.53	$597,745.54
6	$597,745.54	$4,195.29	$3,736	$459.38	$597,286.16
7	$597,286.16	$4,195.29	$3,733	$462.25	$596,823.91
8	$596,823.91	$4,195.29	$3,730	$465.14	$596,358.77
9	$596,358.77	$4,195.29	$3,727	$468.05	$595,890.72
10	$595,890.72	$4,195.29	$3,724	$470.97	$595,419.75
11	$595,419.75	$4,195.29	$3,721	$473.92	$594,945.84
12	$594,945.84	$4,195.29	$3,718	$476.88	$594,468.96
13	$594,468.96	$4,195.29	$3,715	$479.86	$593,989.10
14	$593,989.10	$4,195.29	$3,712	$482.86	$593,506.24
15	$593,506.24	$4,195.29	$3,709	$485.88	$593,020.36
16	$593,020.36	$4,195.29	$3,706	$488.91	$592,531.45
17	$592,531.45	$4,195.29	$3,703	$491.97	$592,039.48
18	$592,039.48	$4,195.29	$3,700	$495.04	$591,544.44
19	$591,544.44	$4,195.29	$3,697	$498.14	$591,046.30
20	$591,046.30	$4,195.29	$3,694	$501.25	$590,545.05
21	$590,545.05	$4,195.29	$3,691	$504.38	$590,040.67
22	$590,040.67	$4,195.29	$3,688	$507.54	$589,533.13
23	$589,533.13	$4,195.29	$3,685	$510.71	$589,022.42
24	$589,022.42	$4,195.29	$3,681	$513.90	$588,508.52
25	$588,508.52	$4,195.29	$3,678	$517.11	$587,991.41
26	$587,991.41	$4,195.29	$3,675	$520.34	$587,471.07
27	$587,471.07	$4,195.29	$3,672	$523.60	$586,947.47
28	$586,947.47	$4,195.29	$3,668	$526.87	$586,420.60
29	$586,420.60	$4,195.29	$3,665	$530.16	$585,890.44
30	$585,890.44	$4,195.29	$3,662	$533.47	$585,356.97
31	$585,356.97	$4,195.29	$3,658	$536.81	$584,820.16
32	$584,820.16	$4,195.29	$3,655	$540.16	$584,280.00
33	$584,280.00	$4,195.29	$3,652	$543.54	$583,736.46
34	$583,736.46	$4,195.29	$3,648	$546.94	$583,189.52
35	$583,189.52	$4,195.29	$3,645	$550.36	$582,639.16
36	$582,639.16	$4,195.29	$3,641	$553.80	$582,085.37
37	$582,085.37	$4,195.29	$3,638	$557.26	$581,528.11
38	$581,528.11	$4,195.29	$3,635	$560.74	$580,967.37
39	$580,967.37	$4,195.29	$3,631	$564.24	$580,403.13
40	$580,403.13	$4,195.29	$3,628	$567.77	$579,835.36
41	$579,835.36	$4,195.29	$3,624	$571.32	$579,264.04
42	$579,264.04	$4,195.29	$3,620	$574.89	$578,689.15
43	$578,689.15	$4,195.29	$3,617	$578.48	$578,110.67
44	$578,110.67	$4,195.29	$3,613	$582.10	$577,528.57
45	$577,528.57	$4,195.29	$3,610	$585.74	$576,942.83
46	$576,942.83	$4,195.29	$3,606	$589.40	$576,353.43
47	$576,353.43	$4,195.29	$3,602	$593.08	$575,760.35
48	$575,760.35	$4,195.29	$3,599	$596.79	$575,163.57

____________________________________________________________________

The remaining balance at end of 4 years = $575,163.57

Refinance: change to 15 years at 6.8%

PMT = Present value of loan 1 - ( 1 + interest rate)^-nt ( interest rate)

PMT = $575,163.57 1 - ( 1 (0.068/12))^-12x30 ( 0.068/12)

PMT = $5,105.63

Total savings = $ 1,510,304.40 - $ 4,195.29 x 48 - $ 5,105.63 x 180

Total savings = $ 389,917.08

______________________________________________________

PERSON 2 - Refinance: For 30 years at 7.1%, reducing monthly payment.

PMT = Present value of loan 1 - ( 1 + interest rate)^-nt ( interest rate)

PMT = $ 600,000 1 - ( 1 + (0.071/12))^-12x30 ( 0.071/12)

PMT = $4,032.19

Total savings =  $ 4,195.29 x 360 - $4,032.19 x 360

Total savings = $ 58,716