In: Finance
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.
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) | |||||||||
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