J said:

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.