Calculating Average Balance for 12% Savings Account: Integrals and Banking

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Homework Statement

A deposit of $2500 is made in a savings account earning 12% interest cpmpounded continuously. Find the average balance in the account during the first two years.

Homework Equations

The Attempt at a Solution

I know I'm suppose to set up an integral from 0 to 2 and then multiple the integral by .5. I was just wondering if someone can explain how to set up the actual integral on the inside. I mean I am not sure what equation I'm using.

 

[HallsofIvy]

Homework Statement

A deposit of $2500 is made in a savings account earning 12% interest cpmpounded continuously.

so the principle is given by P= P_0e^1.12t and the interest is P_0(1- e^{1.12t}. That is what you need to integrate from 0 to 2.

Find the average balance in the account during the first two years.

Homework Equations

The Attempt at a Solution

I know I'm suppose to set up an integral from 0 to 2 and then multiple the integral by .5. I was just wondering if someone can explain how to set up the actual integral on the inside. I mean I am not sure what equation I'm using.