Answer: 20,816.215
Explanation:
Given that:
A deposit of $1000 at 4% interest compounding is defined by the growth function:
v(t) = 1000e^0.04t
Where t = number of years.
Find the average value during the first 40 years (that is, from time 0 to time 40.)
(That is t = 0,...,40)
For ease, we can use a python list comprehension to get our values.
v = [1000*2.7182818**0.04*t for t in range(41)]
V gives a list of the value of the deposit from year 0 till 40 years after the deposit.
Average = sum of compounding deposits / number of years
Sum of compounding deposits = sum(v) = $853464.8344
Number of years = len(v) = 41
Hence, average = $853464.8344 / 41
Average = $20,816.215
