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

Answer:

Their monthly house payment is of $2,184.65.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

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

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(15) = 170000(1 + \frac{0.0575}{1})^{15}$

$A(15) = 393237$

Monthly payment:

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

$M = \frac{393237}{15*12} = 2184.65$

Their monthly house payment is of $2,184.65.