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Sagot :
Answer:
Their monthly house payment is of $2,184.65.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
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, [tex]P = 170,000[/tex]
Value of the loan in 15 years:
15 years means that [tex]t = 15[/tex]
5.75% interest means that [tex]r = 0.0575[/tex]
Compounded yearly, so [tex]n = 1[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(15) = 170000(1 + \frac{0.0575}{1})^{15}[/tex]
[tex]A(15) = 393237[/tex]
Monthly payment:
Total of $393,237 in 15*12 months. So
[tex]M = \frac{393237}{15*12} = 2184.65[/tex]
Their monthly house payment is of $2,184.65.
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