Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump-sum amount as a loan in the beginning, and then you make monthly payments to the lender.

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 12% fixed nominal interest rate (called the loan’s annual percentage rate or APR). Under this loan proposal, your mortgage payment will be_____________ per month.

Respuesta :

Answer:

The mortgage payment will be "$9258".

Explanation:

The given values are:

Principal (P)

= 900000

Interest rate (i)

= [tex]\frac{0.12}{12}[/tex]

= [tex]0.01[/tex]

Total number of monthly payments (n)

= [tex]30\times 12[/tex]

= [tex]360[/tex]

The monthly payment `for the 30 years loan will be:

⇒  [tex]M= P\times \frac{( i\times ( 1 + i ) ^ n )}{( ( ( 1 + i ) ^ n ) - 1 )}[/tex]

On putting the values, we get

         [tex]= 900000\times \frac{( 0.01\times ( 1 + 0.01 ) ^ {360} )}{( ( ( 1 + 0.01 ) ^ {360} ) - 1 )}[/tex]

         [tex]=9257.51[/tex]

         [tex]=9258[/tex]

Now,

The total amount paid will be:

[tex]= 9258\times 360[/tex]

[tex]=33,32,880[/tex] ($)