Answer:
The value of the house after 10 years will be $176,325.
Step-by-step explanation:
The value [tex]y[/tex] of the house appreciates 3.5% each year, which means after 1 year its value will be
[tex]y =\$ 125,000(1.035)[/tex],
after 2 years
[tex]y =\$ 125,000(1.035)(1.035)[/tex],
after 3 years
[tex]y =\$ 125,000(1.035)(1.035)(1.035)[/tex]
and so on.
Thus after nth year the value of the house will be
[tex]y= \$ 125,000(1.035)^n[/tex].
Therefore, after 10 years the house will be worth
[tex]y = \$ 125,000(1.035)^{10}[/tex]
[tex]\boxed{y = \$ 176,325.}[/tex].
