Questions: An automobile purchased for 39,000 is worth 1800 after 6 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year? The value 3 years after it was purchased is .

An automobile purchased for 39,000 is worth 1800 after 6 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?

The value 3 years after it was purchased is .

Transcript text: An automobile purchased for $\$ 39,000$ is worth $\$ 1800$ after 6 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year? The value 3 years after it was purchased is . $\qquad$

Solution

Solution Steps

Step 1: Calculate the Annual Rate of Depreciation

To find the annual rate of depreciation, we use the formula $D = \frac{P - V}{n}$, where $P$ is the initial purchase price, $V$ is the value after $n$ years, and $n$ is the number of years. Substituting the given values, we get $D = \frac{39000 - 1800}{6} = 6200$.

Step 2: Calculate the Value of the Automobile at Year $t$

Next, to find the value of the automobile at year $t$, we use the formula $Value\_at\_t = P - D \times t$. Substituting the given values and the calculated depreciation rate, we get $Value\_at\_t = 39000 - 6200 \times 3 = 20400$.