How can I calculate an accurate Annual Percentage Rate with multiple deposits?

For example: On January 1, an investor deposits $100,000 to an account. Two months later on March 1, the same investor deposits an additional $30,000. On April 30 of the same year, the investor is given a check for $150,000 that repays his total investment (and includes $20,000 profit). Can anyone show me how I would calculate an Annual Percentage Rate? THANKS!!!!How can I calculate an accurate Annual Percentage Rate with multiple deposits?
It is a fairly simple calculation.



$100,000 x 4 months = $400,000 dollar months



$30,000 x 2 months = $60,000 dollar months



Total = $460,000 dollar months



divide by 4 months and you get the average amount in the account was $115,000



The interest rate for four months months = ($20,000 x 100) / $115,000 = 17.39%



To calculate the annual percentage rate you have to decide if you want to compound or not.



Without compounding the annual rate = 17.39% x (12/4) = 52.17%



With compounding the annual rate = (((1 + (17.39 / 100)) ^ (12/4) - 1) x 100 = 61.77%