Question

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

Answer 1

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

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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

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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..