Systematic investment plan interest calculation

How can I calculate the effective compound annual growth rate (http://en.wikipedia.org/wiki/Compound_annual_growth_rate) for a systematic investment plan (http://en.wikipedia.org/wiki/Systematic_Investment_Plan) ? It has to take into account compound interest, various formulae of which are given on http://en.wikipedia.org/wiki/Compound_interest#Mathematics_of_interest_rates but I am not able to use them for regular monthly investments.

Suppose I deposit 1000 (P) dollars every month for 5 (t) years (so I deposit 60,000 over 5 years) and the final amount that I get back is 75,000 (A). What is the effective interest rate (r) for me if compounding is taken into account?

If I know the monthly interest rate r (as fraction), I can use following formulae for each deposit and add up the amounts:

``````A = P*(1+r)^t
``````

or for continuous compounding:

``````A = P*e^(r*t)
``````

But how to calculate r when other values are known? Thanks for your help.

• Important missing information: is the \$75000 present at the moment of the last \$1000 payment, or one month after that last payment" – DJohnM Jul 7 '14 at 16:21
• Since this is an investment plan it is an annuity-due, with payments at the beginning of each period. – Chris Degnen Jul 8 '14 at 7:46 