From: Ronald Raygun 
Subject: Re: Calculating Interest Rate on Regular Savings
Newsgroups: uk.finance
Date: Mon, 23 Jan 2006 12:34:38 GMT

J C wrote:

> If I know how much I paid in to an investment (£x per week for 10 years)
> and what the value is at maturity, how do I work out what the effective
> rate of interest was over the period? I want to see just how badly this
> did compared to sticking the money in a savings account.

The value at week 0 is 0, at week 1 £x, at week 2 f*£X + £x, where
f is one plus the weekly rate of interest.

Hence at week 520, the value is £x times the sum of all the powers
of f from 0 to 519.  If the value is £y, then the following equality
holds:

£y = £x * (f^520 - 1)/(f-1)

All you need to do is solve for f.

Unfortunately this is not possible algebraically (but if Tim wants to
claim otherwise, I'd be delighted to hear how).  So the simplest thing
to do is guess a value for f, compute the right hand side, and compare
it with £y.  If the answer is too big, your f was too big, so reduce it
a bit for your next guess.

Having found f, raise it to the power 52 and subtract one, and that's
your annual effective rate.