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%
(a) Find the average amount earned per year between the 5th year and the 10th year.
To find the average amount earned per year between the 5th year and the 10th year, we need to find the value of the investment after 5 years and after 10 years and then calculate the average amount earned per year during this time period.
After 5 years:
y(5) = 5000 * e^(0.04*5)
y(5) = 5000 * e^(0.2)
y(5) = 5000 * 1.221402
y(5) = 6107.01
After 10 years:
y(10) = 5000 * e^(0.04*10)
y(10) = 5000 * e^(0.4)
y(10) = 5000 * 1.491825
y(10) = 7459.13
Now, we calculate the average amount earned per year between the 5th year and the 10th year:
Total amount earned = 7459.13 - 6107.01 = $1352.12
Number of years = 10 - 5 = 5
Average amount earned per year = Total amount earned / Number of years
Average amount earned per year = 1352.12 / 5
Average amount earned per year ≈ $270.42
Therefore, the average amount earned per year between the 5th year and the 10th year is approximately $270.42.