An oil painting is worth $400. Its value increases by 7% each year(compounded annually)
What is the value of the painting after 6 years? How would the graph change of the initial value of the oil painting was more than $400? Less than $400?
after n years, its value is
400(1.07)^n
To find the value of the painting after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final value of the painting
P = the initial value of the painting
r = the interest rate
n = the number of times the interest is compounded per year
t = the number of years
Given that the initial value of the painting is $400, the interest rate is 7% (0.07), and the interest is compounded annually, we can substitute the values into the formula:
A = 400(1 + 0.07)^6
Calculating this expression will give us the value of the painting after 6 years.
A = 400(1.07)^6
≈ 540.808
So, the value of the painting after 6 years is approximately $540.81.
Now, let's consider how the graph would change if the initial value of the oil painting was more than $400 or less than $400:
1. More than $400: If the initial value of the painting is greater than $400, let's say $500, then the value of the painting after 6 years would be higher still. This is because the 7% increase is applied to a larger base value ($500). As a result, the value of the painting after 6 years would be higher than $540.81.
2. Less than $400: If the initial value of the painting is less than $400, let's say $300, then the value of the painting after 6 years would be lower. This is because the 7% increase is applied to a smaller base value ($300). Consequently, the value of the painting after 6 years would be less than $540.81.
In summary, if the initial value of the oil painting is more than $400, the value after 6 years would be higher, and if it is less than $400, the value after 6 years would be lower.