An antique dresser was purchased for $3500 in 1985. The dresser appreciates at a rate of 7%
per year. Find the value of the dresser in 2002.
To find the value of the dresser in 2002, we need to calculate the appreciation amount for each year from 1985 to 2002 and add it to the initial value of $3500.
The annual appreciation rate is 7%, which means the value of the dresser increases by 7% every year.
To calculate the appreciation for each year, we multiply the previous year's value by 0.07 and add it to the previous year's value.
Let's break down the calculation year by year:
- In 1986, the value of the dresser is $3500 + ($3500 * 0.07) = $3500 + $245 = $3745.
- In 1987, the value of the dresser is $3745 + ($3745 * 0.07) = $3745 + $262.15 = $4007.15.
- In 1988, the value of the dresser is $4007.15 + ($4007.15 * 0.07) = $4007.15 + $280.5 = $4287.65.
We continue this process until we reach 2002:
- In 2002, the value of the dresser is $3500 + ($3500 * 0.07)^17.
- Evaluating this expression, we find that the value of the dresser in 2002 is approximately $9058.73.
Therefore, the value of the antique dresser in 2002 is approximately $9058.73.