Question

A family wants to purchase a house that costs $140,000. They plan to take out a $100,000 mortgage on the house and put $40,000 as a down payment. The bank informs them that with a 15-year mortgage, their monthly payment would be $730.27, and with a 30-year mortgage, their monthly payment would be $530.29. Determine the amount they would save on the cost of the house if they selected the 15-year mortgage."

a) $5,894.80
b) $6,884.80
c) $7,894.80
d) $8,894.80

Answer 1

When comparing the total payments of a 15-year mortgage versus a 30-year mortgage, the family would save $59,455.80 by choosing the 15-year mortgage. However, this savings amount does not match any of the options (a-d) provided in the question.

Step-by-step explanation:

To find the amount the family would save on the cost of the house by selecting the 15-year mortgage instead of the 30-year mortgage, we'll compare the total payments for both options. For the 15-year mortgage at $730.27 per month, the total payment over 15 years would be:15 years × 12 months/year × $730.27/month = $131,448.60For the 30-year mortgage at $530.29 per month, the total payment over 30 years would be:30 years × 12 months/year × $530.29/month = $190,904.40Now, subtract the total cost of the 15-year mortgage from the total cost of the 30-year mortgage to find the savings:$190,904.40 - $131,448.60 = $59,455.80

However, none of the provided options (a-d) match the calculated savings of $59,455.80, so it's possible there was a mistake in the question or the options given.To determine the amount the family would save on the cost of the house if they selected the 15-year mortgage, we need to calculate the total cost of each mortgage option.30-year Mortgage:Monthly payment: $530.2Total payment over 30 years: $530.29 x 12 x 30 = $190,924.40Total cost of the house: $190,924.40 + $40,000 down payment = $230,924.4015-year Mortgage:Monthly payment: $730.27Total payment over 15 years: $730.27 x 12 x 15 = $131,444.20Total cost of the house: $131,444.20 + $40,000 down payment = $171,444.20Amount saved on the cost of the house: $230,924.40 - $171,444.20 = $59,480.20Therefore, the family would save $59,480.20 on the cost of the house if they selected the 15-year mortgage. The answer is not one of the provided options.