The function given by y = f(x) shows the value of $5000 invested at 4% interest compounded continuously, x years after the money was originally invested.
(Round your answers to the nearest cent.)
Value of $5000 with Continuous Compounding at 4%
(b) Find the average amount earned per year between the 20th year and the 25th year.
To find the average amount earned per year between the 20th and 25th year, we first need to find the value of the investment at both time points.
First, we calculate the value at the 20th year:
y(20) = 5000 * e^(0.04*20)
y(20) = 5000 * e^0.8
y(20) = 5000 * 2.22554092850
y(20) = $11127.70
Next, we calculate the value at the 25th year:
y(25) = 5000 * e^(0.04*25)
y(25) = 5000 * e^1
y(25) = 5000 * 2.71828182846
y(25) = $13591.41
Now, we can find the average amount earned per year between the 20th year and the 25th year:
Average amount earned per year = (y(25) - y(20)) / (25 - 20)
Average amount earned per year = ($13591.41 - $11127.70) / 5
Average amount earned per year = $646.14 / 5
Average amount earned per year = $129.23
Therefore, the average amount earned per year between the 20th year and the 25th year is $129.23.