# working out yield / growth rate on monthly premiums

Hi, I wonder if anyone can help with this.
Assuming I had been paying £25 per month into a plan for ten years (say £3,000 in premiums in total) and the value at year ten is say £5,000 ho w would I work out the annualised growth rate ?
This is pretty easy to work out if it was just a single premium paid at the outset. It is also easy to project forward. However, as monthly premiums e ach have their own separate timeline, is there a formula that would give an approximate answer to such a question ?
I think the EXCEL rate function may work, but I'm looking for an actual mat hematical formula.
Any ideas ?
Thanks Neil.

I tried doing it the hard way, and ended up with a polynomial of order 120 to solve.
But I think you can get an approximate result: on average over ten years, each £25 premium attracts interest over 60 months (the range is from 1 to 120 months). The formula is easy:
25*R^60 = 5000/3000
(where R is the monthly growth rate, eg. 1.005, and ^ means to the power of). Then, R is the 60th root of 1.667, or 1.0085. The monthly interest rate is 0.85%, or 10.8% annually.
(This assumes interest is compounded monthly rather than annually, however the difference is small. To do it annually, a similar formula is:
300*R^5 = 5000/3000, so R is the 5th root of 1.667, or 1.1076 (10.8% annual interest).)
(BTW what sort of plan gives you a nearly 11% growth rate?)