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?
To calculate 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 future value of the painting
P = the initial value of the painting
r = the interest rate per compounding period (expressed as a decimal)
n = the number of compounding periods per year
t = the number of years
Given in this case:
P = $400 (initial value)
r = 7% (interest rate per year, compounded annually)
n = 1 (since it is compounded annually)
t = 6 (number of years)
Plugging these values into the formula, we have:
A = 400(1 + 0.07/1)^(1*6)
A = 400(1.07)^6
A ≈ $586.87
Therefore, the value of the painting after 6 years would be approximately $586.87.
Now, let's consider how the graph would change if the initial value of the oil painting was more or less than $400:
1. If the initial value was more than $400:
In this case, the initial point on the graph would be higher, representing the higher value of the painting. But the shape and slope of the graph would remain the same, i.e., the value would still increase by 7% each year.
2. If the initial value was less than $400:
In this case, the initial point on the graph would be lower, representing the lower value of the painting. Again, the shape and slope of the graph would be the same, so the value would still increase by 7% each year.
In summary, the graph would change vertically based on the initial value, but the increase rate would remain the same.