Question

An Impressionist painting increases in value

at an average rate of 9% a year. If the origi-
nal cost of the painting to the Museum of
Art was $1500, what was the value of the
painting (to the nearest dollar) at the end of
a 20-year holding period?

Answer 1

A = $8406.6

Explanation:

Given:

Average rate
`r=9\%`

Initial cost of painting
`a = \$1500`

Time
`t = 20\ years`

We need to find the final amount of painting at the end of a 20-year.

Solution:

Using Exponential Growth rate formula as:

`A = a(1+r)^t` ----------(1)

Where:

A = Final amount

a = Initial amount.

r = Rate as a decimal.

t = Time.

Now, we substitute all given values in equation 1.

`A = 1500(1+0.09)^(20)`

`A = 1500(1.09)^(20)`

Substitute
`1.09^(20) = 5.60` in above equation.

`A = 1500* 5.60`

A = $8406.62

Therefore, value of the painting at the end of a 20-year A = $8406.6