Question

A deposit of $1000 at 4% interest compounded continuously will grow to v(t) = 1000 e^0.04 dollars after t year. Find the average value during the first 40 years (that is, from time 0 to time 40.)

Answer 1

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