Question

You’ve decided to buy a house that is valued at $1 million. You have $100,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $900,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan’s annual percentage rate or APR). Under this loan proposal, your mortgage payment will be per month. (Note: Round the final value of any interest rate used to four decimal places.)

Answer 1

Answer:

Ans. Your mortgage payment will be $7,898.14 per month.

Explanation:

Hi, first, we need to find the equivalent effective monthly rate for 10% APR, that is 10% / 12= 0.8333% effective monthly.

After that, we have to present the periods of the loan in months, that is 30 years * 12 = 360 months

Now, we are ready to find the answer, we need to use the following equation and solve for "A"

$Present Value=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

Where:

A= our answer

r= interest rate (0.8333% effective monthly)

n= periods of periodic payment (in our case 360 months)

The math to this is as follows.

$900,000=\frac{A((1+0.008333)^{360}-1) }{0.008333(1+0.008333)^{360} }$

$900,000=A(113.95082)$

$\frac{900,000}{113.95082} =A$

$A=7,898.14$

Best of luck.