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?
i don't understand what @Steve means
To find the value of the painting after 6 years, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the final amount (or value of the painting)
P is the initial amount (or value of the painting)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the initial amount (P) is $400, the annual interest rate (r) is 7% (or 0.07 as a decimal), and the number of times interest is compounded per year (n) is 1 (since it's compounded annually). We need to calculate the final amount (A) after 6 years (t = 6).
Using the formula, we have:
A = 400(1 + 0.07/1)^(1*6)
A = 400(1 + 0.07)^6
A = 400(1.07)^6
A ≈ 598.97
Therefore, the value of the painting after 6 years would be approximately $598.97.
Now, let's consider the graph of the initial value of the oil painting if it was more or less than $400:
If the initial value of the painting was more than $400, let's say $500, the graph would start at a higher point on the y-axis, representing a higher initial value. However, as the value increases by 7% each year, the rate of increase remains the same, so the overall shape of the graph would remain the same, just shifted upwards.
On the other hand, if the initial value of the painting was less than $400, let's say $300, the graph would start at a lower point on the y-axis, representing a lower initial value. As the value of the painting still increases by 7% each year, the rate of increase remains the same, so the overall shape of the graph would remain the same, just shifted downwards.