Question

Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will the value of the house be after 10 years?

Answer 1

The value of the house after 10 years will be $176,325.

Explanation:

The value
`y` of the house appreciates 3.5% each year, which means after 1 year its value will be

`y =\$ 125,000(1.035)`,

after 2 years

`y =\$ 125,000(1.035)(1.035)`,

after 3 years

`y =\$ 125,000(1.035)(1.035)(1.035)`

and so on.

Thus after nth year the value of the house will be

`y= \$ 125,000(1.035)^n`.

Therefore, after 10 years the house will be worth

`y = \$ 125,000(1.035)^(10)`

`\boxed{y = \$ 176,325.}`.