Question

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.

Answer 1

The mortgage payment will be "$9258".

Step-by-step explanation:

The given values are:

Principal (P)

= 900000

Interest rate (i)

=
`(0.12)/(12)`

=
`0.01`

Total number of monthly payments (n)

=
`30* 12`

=
`360`

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

⇒
`M= P* (( i* ( 1 + i ) ^ n ))/(( ( ( 1 + i ) ^ n ) - 1 ))`

On putting the values, we get

`= 900000* \frac{( 0.01* ( 1 + 0.01 ) ^ {360} )}{( ( ( 1 + 0.01 ) ^ {360} ) - 1 )}`

`=9257.51`

`=9258`

Now,

The total amount paid will be:

`= 9258* 360`

`=33,32,880` ($)