Question

A home is purchased for $ 794,000 with a 16% down payment. Find the monthly payment if the mortgage is 7.22% for 19 years. Round your answer to two

decimal places, if necessary,

Answer 1

The monthly payment will be of $11,485.37

Explanation:

Compound interest:

The compound interest formula is given by:

`A(t) = P(1 + (r)/(n))^(nt)`

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

A home is purchased for $ 794,000 with a 16% down payment.

So the value of the loan, that is, the amount subject to interest, will be given by:

`P = (1-0.16)*794000 = 0.84*794000 = 666960`

How much will the interest accumulate to?

7.22% of interest means that
`r = 0.0722`

19 means means that
`t = 19`

Monthly means that
`n = 12`

So

`A(t) = P(1 + (r)/(n))^(nt)`

`A(t) = 666960(1 + (0.0722)/(12))^(12*19)`

`A(t) = 2618664.5`

Monthly payment:

2618664.5 divided in 19*12 payments. So

2618664.5/(19*12) = 11485.37

The monthly payment will be of $11,485.37