Mortgage Payment You currently have a 30-year fixed rate mortgage with an annual interest rate of...

Mortgage Payment

You currently have a 30-year fixed rate mortgage with an annual interest rate of 6%. You have had the mortgage 4 years, and on September 1, 2015 you made your 48th payment. The original principal amount was $280,000 and you monthly payment, without taxes and insurance, are $1,678.74 per month, computed using the Excel function =PMT(0.5%,360,280000,0,0).

Starting with your original mortgage your banker calls and says that you could refinance your existing mortgage (6% rate, 30-year original term) into a 15-year mortgage at 3.2%. Assume you will refinance the current principal (the current remaining loan balance).

QUESTION:

What would the payments be with the 15-year mortgage?

Compare the total interest paid over the life of both loans: the 30-year loan and the new 15-year loan.

Expert Solution

period	360
Interest rate per month	0.50%
Principle amount	280000
Monthly intesest	($1,678.74)

	Computation of outstanding balance after 48 month
	month	Loan outstanding at beginning	interest on outstanding balance	Monthly instalment paid	Loan outstanding at the end
	0	280,000.0	1,400.0	(1,678.7)	279,721.3
	1	279,721.3	1,398.6	(1,678.7)	279,441.1
	2	279,441.1	1,397.2	(1,678.7)	279,159.6
	3	279,159.6	1,395.8	(1,678.7)	278,876.6
	4	278,876.6	1,394.4	(1,678.7)	278,592.3
	5	278,592.3	1,393.0	(1,678.7)	278,306.5
	6	278,306.5	1,391.5	(1,678.7)	278,019.3
	7	278,019.3	1,390.1	(1,678.7)	277,730.7
	8	277,730.7	1,388.7	(1,678.7)	277,440.6
	9	277,440.6	1,387.2	(1,678.7)	277,149.0
	10	277,149.0	1,385.7	(1,678.7)	276,856.0
	11	276,856.0	1,384.3	(1,678.7)	276,561.6
	12	276,561.6	1,382.8	(1,678.7)	276,265.6
	13	276,265.6	1,381.3	(1,678.7)	275,968.2
	14	275,968.2	1,379.8	(1,678.7)	275,669.3
	15	275,669.3	1,378.3	(1,678.7)	275,368.9
	16	275,368.9	1,376.8	(1,678.7)	275,067.0
	17	275,067.0	1,375.3	(1,678.7)	274,763.6
	18	274,763.6	1,373.8	(1,678.7)	274,458.7
	19	274,458.7	1,372.3	(1,678.7)	274,152.3
	20	274,152.3	1,370.8	(1,678.7)	273,844.3
	21	273,844.3	1,369.2	(1,678.7)	273,534.8
	22	273,534.8	1,367.7	(1,678.7)	273,223.7
	23	273,223.7	1,366.1	(1,678.7)	272,911.1
	24	272,911.1	1,364.6	(1,678.7)	272,596.9
	25	272,596.9	1,363.0	(1,678.7)	272,281.1
	26	272,281.1	1,361.4	(1,678.7)	271,963.8
	27	271,963.8	1,359.8	(1,678.7)	271,644.9
	28	271,644.9	1,358.2	(1,678.7)	271,324.3
	29	271,324.3	1,356.6	(1,678.7)	271,002.2
	30	271,002.2	1,355.0	(1,678.7)	270,678.5
	31	270,678.5	1,353.4	(1,678.7)	270,353.1
	32	270,353.1	1,351.8	(1,678.7)	270,026.2
	33	270,026.2	1,350.1	(1,678.7)	269,697.6
	34	269,697.6	1,348.5	(1,678.7)	269,367.3
	35	269,367.3	1,346.8	(1,678.7)	269,035.4
	36	269,035.4	1,345.2	(1,678.7)	268,701.8
	37	268,701.8	1,343.5	(1,678.7)	268,366.6
	38	268,366.6	1,341.8	(1,678.7)	268,029.7
	39	268,029.7	1,340.1	(1,678.7)	267,691.1
	40	267,691.1	1,338.5	(1,678.7)	267,350.8
	41	267,350.8	1,336.8	(1,678.7)	267,008.8
	42	267,008.8	1,335.0	(1,678.7)	266,665.1
	43	266,665.1	1,333.3	(1,678.7)	266,319.7
	44	266,319.7	1,331.6	(1,678.7)	265,972.6
	45	265,972.6	1,329.9	(1,678.7)	265,623.7
	46	265,623.7	1,328.1	(1,678.7)	265,273.1
	47	265,273.1	1,326.4	(1,678.7)	264,920.7
	48	264,920.7	1,324.6	(1,678.7)	264,566.6
			66,824.9

	Outstanding loan balance = 264,566.6

	Payment with 15 year loan @ 3.2% interest can be calculated as below
	Period = 15*12	180
	Monthly interest rate =3.2%/12	0.2667%
	Outstanding loan	264567
	Payment =	=PMT(0.2667%,180,264567,0,0)
	Hence payment =	($1,852.60)

	Interest paid
	Interest paid on 30 year loan closed after 4 year =			66,824.9
	Interest paid on 15 year loan

	we can use FV formula in excel to compute FV of the annuity 1852.6 for 15 year paid monthly @ 0.2667% per month

	Future value of loan	=FV(0.2667%,180,-1852.6,0,0)
	Future value of loan	427,299
	Less Principle amount	264567
	interest paid on 15 year loan	162,732

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