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

Here is quick demo calculation. The effective interest rate comes out at 8.85525 %

The syntax is Mathematica.

enter image description here

  • This is exactly what I wanted. Thanks. Can you give R language code for this? – rnso Jul 7 '14 at 14:12
  • @rnso - sorry, I can't help there. – Chris Degnen Jul 7 '14 at 14:19

You are dealing with regular, periodic payments. There are formulas in the source you cite for this situation, but none of those formulas will allow you to find the interest rate necessary to turn a series of regular payments into a specified final amount. The only way is to use trial and error; trying different interest rates with the given payment information until you find the one producing the desires amount.

Fortunately, many online calculators are available to carry out these trial and error calculations. More simply, Excel supplies a function, RATE, that will give the interest rate for a given series of payments.

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