Question

Two years ago you took out a mortgage at 4.5%. The initial balance of the loan was $200,000 and it was for 25 years (300 months.) Today, you observe that you could take out a new loan at 4.25% (with a 300 month term), but you would have to pay $5,000 in closing and other fees.

What is the current value of the loan (liability from your perspective)?

*Note: The answer is $195,579.52. I want to know how to get the answer with a financial calculator.

Answer 1

First we calculate using PMT

I/Y = 4.5%/12 = 0.375%

N = 300

PV = 200000

FV = 0

PMT = -1111.66

Then use simple maths to calculate interest per month and calculate resulting principal and add $5000 at the end to reach the total loan liability today.

	4.5%/12	0.3750%
	Loan Balance	PMT	Interest for the month	Principal paid in the month
1	200000	₹ -1,111.66	750.00 (200000*1*0.375%)	₹ -361.66 (PMT + Interest)
2	₹ 1,99,638.34	₹ -1,111.66	748.64	₹ -363.02
3	₹ 1,99,275.31	₹ -1,111.66	747.28	₹ -364.38
4	₹ 1,98,910.93	₹ -1,111.66	745.92	₹ -365.75
5	₹ 1,98,545.18	₹ -1,111.66	744.54	₹ -367.12
6	₹ 1,98,178.06	₹ -1,111.66	743.17	₹ -368.50
7	₹ 1,97,809.56	₹ -1,111.66	741.79	₹ -369.88
8	₹ 1,97,439.69	₹ -1,111.66	740.40	₹ -371.27
9	₹ 1,97,068.42	₹ -1,111.66	739.01	₹ -372.66
10	₹ 1,96,695.76	₹ -1,111.66	737.61	₹ -374.06
11	₹ 1,96,321.71	₹ -1,111.66	736.21	₹ -375.46
12	₹ 1,95,946.25	₹ -1,111.66	734.80	₹ -376.87
13	₹ 1,95,569.38	₹ -1,111.66	733.39	₹ -378.28
14	₹ 1,95,191.10	₹ -1,111.66	731.97	₹ -379.70
15	₹ 1,94,811.40	₹ -1,111.66	730.54	₹ -381.12
16	₹ 1,94,430.28	₹ -1,111.66	729.11	₹ -382.55
17	₹ 1,94,047.73	₹ -1,111.66	727.68	₹ -383.99
18	₹ 1,93,663.74	₹ -1,111.66	726.24	₹ -385.43
19	₹ 1,93,278.32	₹ -1,111.66	724.79	₹ -386.87
20	₹ 1,92,891.45	₹ -1,111.66	723.34	₹ -388.32
21	₹ 1,92,503.12	₹ -1,111.66	721.89	₹ -389.78
22	₹ 1,92,113.34	₹ -1,111.66	720.43	₹ -391.24
23	₹ 1,91,722.10	₹ -1,111.66	718.96	₹ -392.71
24	₹ 1,91,329.40	₹ -1,111.66	717.49	₹ -394.18
25	₹ 1,90,935.22