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.
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.
1 answer