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?
V = Vo(1+r)^6
Vo = 400
r = 0.07
V = ?
To calculate the value of the painting after 6 years, we need to use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = final amount (value of the painting after 6 years)
P = principal amount (initial value of the painting)
r = annual interest rate (7% or 0.07 in decimal form)
n = number of times interest is compounded per year (since it's compounded annually, n = 1)
t = number of years (6 years in this case)
Substituting the given values into the formula:
A = 400(1 + 0.07/1)^(1*6)
A = 400(1.07)^6
A ≈ 598.22
So the value of the painting after 6 years is approximately $598.22.
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.
If the initial value of the painting is more than $400, it would simply shift the entire graph upwards. This means that with each passing year, the value of the painting would be even higher compared to the original $400 value.
On the other hand, if the initial value of the painting is less than $400, it would shift the graph downwards. This means that, over time, the value of the painting would still increase from its initial lower value, but it would remain lower compared to the original $400 value.
In both cases, the rate of increase would still be 7% per year (compounded annually), but the starting point would be different due to the initial value of the painting.