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
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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..
The given function is f(x)=2x^3+2x^2-x. In this case, the highest degree among the terms is 3. According to the Fundamental Theorem of Algebra, the number of zeros or roots of the equation is equal to the highest degree among the terms. Hence for every value of y, there are 3 equivalent x's. The answer thus is B. It is a many-to-one function.
