Question

You buy a house for $180,000 that depreciates at a rate of

3% each year. How much is the house worth after 5 years?
Round your answer to the nearest cent.

Answer 1

To find the value of a house after 5 years with an annual depreciation rate of 3%, you use the exponential decay formula, which calculates the future value to be approximately $154,572.04.

Step-by-step explanation:

To determine how much a house worth $180,000 will depreciate after 5 years at a 3% annual rate, we can use the formula for exponential decay: V = P(1 - r)^t, where:

• V is the future value of the house,
• P is the present value ($180,000),
• r is the annual depreciation rate (0.03),
• t is the number of years (5).

Plugging in the values, we get:

V = $180,000(1 - 0.03)^5

V = $180,000(0.97)^5

V = $180,000(0.858734025)

V = $154,572.04

After 5 years, the house would be worth approximately $154,572.04.