Suppose you deposit $5000 at 9% interest compounded continuously. Find the average value of your account during the first 2 years.

Answer 1

The word continuous indicates that we have to use: A=Pe^(rt)

A is the new amount

P is the principal investment (or initial amount)

r is the rate (in decimal form)

t is the time (in years)

When t=0

A = 5000e^(.09*0)

A= 5000

When t=2

A = 5000e^(.09*2)

A = 5986.09

To find the average, we add the values and divide by the number of years.

(5000 + 5986.09) / 2

5493.04