A family wants to purchase a house that costs $165 comma 000. They plan to take out a $125 comma 000 mortgage on the house and
put $40 comma 000 as a down payment. The bank informs them that with a 15-year mortgage their monthly payment would be $740.18 and with a 30-year mortgage their monthly payment would be $518.33. Determine the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage
Case A: 15-year mortgage The family puts $40,000 as a down payment. They pay $740.18 per month for 15 years, which is the same as 180 months (15*12 = 180). So they pay 180*740.18 = $133,232.40 on top of the $40,000 down payment. The total cost of the home is 40,000+133,232.40 = 173,232.40
Since we'll use this value later, let's call it m. So m = 173,232.40
-----------------------------------------------
Case B: 30-year mortgage
Down payment = $40,000 Monthly Payment = $518.33 Number of months = (number of years)*12 Number of months = (30)*12 Number of months = 360 Total cost = (number of months)*(monthly payment) + (down payment) Total cost = 360*518.33+40,000 Total cost = $226,598.80
Call this n. So n = 226,598.80
-----------------------------------------------
Comparison:
With the 15-year mortgage, the total cost was m = 173,232.40 With the 30-year mortgage, the total cost was n = 226,598.80
How much does the family save if they go with the 15-year mortgage? Subtract the values n - m = 226,598.80 - 173,232.40 = 53,366.4
The family saves $53,366.40
The 15-year mortgage is the better option assuming the family can afford the larger monthly payment..
