Question

$100 is deposited in the bank at 5% interest compounded continuously. What will be the average value of the money in the account during the next 20 years?

Answer 1

The average value is the average of the values from year 0 to year 19.
The value of the principal $100 remains from day 0 to 364, that is why the choice of years 0 to 19.
The values are:
100.0105.0110.25115.76121.55127.62134.0140.71147.74155.13162.88171.03179.58188.56197.99207.89218.28229.2240.66252.69
for an average value of $165.33