515,174 views
20 votes
20 votes
I WILL GIVE U A CROWN.......

Liz is buying a home for $426,000. She is making a 22% down payment and financing the rest with a 20-year loan at 5.25% interest.



What will her total payment for the home be? Round your answer to the nearest dollar.

$598,424


$600,306


$610,442


$631,057

User Ganj Khani
by
3.2k points

1 Answer

9 votes
9 votes

Answer: Likely it's choice D)

See below for the explanation why

========================================================

down payment = 22% of home value

down payment = 22% of $426,000

down payment = 0.22*426,000

down payment = 93,720 dollars

The remaining amount mortgaged (i.e. loaned out) is

home value - (down payment) = 426,000 - 93,720 = 332,280

----------------

The monthly payment formula is

P = (L*i)/(1 - (1+i)^(-n))

where,

  • P = monthly payment
  • L = amount loaned
  • i = monthly interest rate in decimal form
  • n = number of months

In this case,

  • L = 332,280 dollars
  • i = 0.0525/12 = 0.004375 which is exact without any rounding
  • n = 20*12 = 240 months (equivalent to 20 years)

Plugging those three values into the formula mentioned gets us the following:

P = (L*i)/(1 - (1+i)^(-n))

P = (332,280*0.004375)/(1 - (1+0.004375)^(-240))

P = 2,239.0493959316

P = 2,239.05

Multiply this monthly payment by the 240 months mentioned.

2,239.05*240 = 537,372

This is the total amount paid back (principal + interest)

Add on the down payment to find out how much money total is handed over: 537,372 + 93,720 = 631,092

Unfortunately $631,092 is not listed as one of the answer choices. The closest would be D) $631,057

I'm not sure if I made a rounding error somewhere, or perhaps your teacher is using an amortization table. It's also possible your teacher made a typo somewhere. I'd ask them for clarification.

User Dennis Alexander
by
2.7k points