Calculating Interest Rate on Regular Savings

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:

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.

Tried that and got an effective rate of 0.9%. (0.896701% to be more precise.)

I used Excel and put the formula in as =5*(A1^520-1)-1/(A1-1) where A1 was used to hold the figure for f.

The payment was 5 per month for 10 years and the payout was 2926. (or 326 more than I paid in!) Does that look about right?

I know it's not a lot of money but I did want to see how badly it had done.

Thanks for your help

John

There is a typo there. You didn't really have the extra -1 between the ) and / did you?

No, I get f=1.00044665 which makes the annual rate about 2.35%.

gnuplot> f(x)=5*(x**520-1)/(x-1) gnuplot> print f(1.00044665)

There was a typo, not sure how that got there but it was also present on the spreadsheet. I think it probably sneaked in using Cut and Paste. Fixed that and the figures now match yours.

Thanks for all the help, now I know it was as a bad investment and not the disaster my figures made it!

The formula has now been saved for future use.