Question

You are buying a house and the mortgage company offers to let you pay a​ "point"

​(1.0 %

of the total amount of the​ loan) to reduce your APR from

6.46 %

to

6.21 %

on your

$ 403 comma 000

​,

30

​-year

mortgage with monthly payments. If you plan to be in the house for at least five​ years, should you do​ it? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The monthly mortgage payment at 6.46% APR is:

The monthly mortgage payment at 6.21% APR is:

The lower interest rate on the mortgage results in monthly savings of:

The PV of the monthly savings is:

The balance of the mortgage at the end of five years at 6.46% APR is:

The balance of the mortgage at the end of five years at 6.21% APR is:

The principle reduction due to the lower interest rate is:

The PV of the principle reduction is:

The net benefit or cost is:

The net benefit is (positive or negative); therefore, you (should or should not) pay the point.

Answer 1

		The monthly mortgage payment at 6.46% APR
	Rate	Monthly interest =(6.46/12)%=	0.53833%
	Nper	Number of months of mortgage	360	(30*12)
	Pv	Amount of loan	$403,000
	PMT	Monthly mortgage payment	$2,536.64	(Using PMT function of excel with Rate =0.53833%, Nper=360, Pv=-403000)
		The monthly mortgage payment at 6.21% APR
	Rate	Monthly interest =(6.21/12)%=	0.51750%
	Nper	Number of months of mortgage	360	(30*12)
	Pv	Amount of loan	$403,000
	PMT	Monthly mortgage payment	$2,470.87	(Using PMT function of excel with Rate =0.51750%, Nper=360, Pv=-403000)
		The lower interest rate on the mortgage results in monthly savings of	$65.78	(2536.64-2470.87)
		PV of the monthly savings:
	Pmt	Monthly Savings	$65.78
	Rate	Monthly interest =(6.21/12)%=	0.51750%
	Nper	Number of months of savings	60	(5*12)
	PV	PV of the monthly savings:	$3,385.20	(Using PV function of excel with Rate =0.51750%, Nper=60, Pmt=-65.78)
		The balance of the mortgage at the end of five years at 6.46% APR
	Rate	Monthly interest =(6.46/12)%=	0.53833%
	Nper	Number of months of mortgage	60
	Pmt	Monthly mortgage payment	$2,536.64
	FV1	Future Value at end of 5 years	$179,089.73	(Using FV function of excel with Rate =0.53833%, Nper=60, Pmt=-2536.64)
	FV2	Future Value of loan at end of 5 years	$556,167.92	(Using FV function of excel with Rate =0.53833%, Nper=60, Pv=-403000)
	FV2-FV1	Loan Balance at end of 5 years	$377,078.19
		The balance of the mortgage at the end of five years at 6.21% APR
	Rate	Monthly interest =(6.21/12)%=	0.51750%
	Nper	Number of months	60
	Pmt	Monthly mortgage payment	$2,470.87
	FV1	Future Value at end of 5 years	$173,325.98	(Using FV function of excel with Rate =0.51750%, Nper=60, Pmt=-2470.87)
	FV2	Future Value of loan at end of 5 years	$556,167.92	(Using FV function of excel with Rate =0.53833%, Nper=60, Pv=-403000)
	FV2-FV1	Loan Balance at end of 5 years	$382,841.94
		principle reduction due to the lower interest rate	$5,763.76	(382841.94-377078.19)