Question

A home was bought in 2011 for $200,000, and its value appreciates by 5% every single year. The value of the home t years since 2011 is given by the formula V(t)=200,000(1.05)t. Find the value of the home in the year 30 years after it was bought. Round your answer to the nearest cent.

Answer 1

$864,388.48

Explanation:

The value of the home t years since 2011 is given by the formula:

`V\left(t\right)=200000\left(1.05\right)^t`

To find the value of the home in the year 30 years after it was bought, substitute 30 for t in the formula:

`\begin{gathered} V\left(30\right)=200,000\left(1.05\right)^(30) \\ \approx\$864,388.48 \end{gathered}`

The value of the home is $864,388.48 (correct to the nearest cent).