Question

a family buys a new home for $212,500 and pays a 20% down payment ($42,500). if the mortgage is for 15 years at 5.75% interest which is their monthly house payment

Answer 1

Their monthly house payment is of $2,184.65.

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 family buys a new home for $212,500 and pays a 20% down payment ($42,500).

This means that the loan is of 212,500 - 42,500 = $170,000, that is,
`P = 170,000`

Value of the loan in 15 years:

15 years means that
`t = 15`

5.75% interest means that
`r = 0.0575`

Compounded yearly, so
`n = 1`

Then

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

`A(15) = 170000(1 + (0.0575)/(1))^(15)`

`A(15) = 393237`

Monthly payment:

Total of $393,237 in 15*12 months. So

`M = (393237)/(15*12) = 2184.65`

Their monthly house payment is of $2,184.65.