Is there an easy formluae for this?

homersimpson_3

x transfers £100 on 31st of each month into account paying 5% gross. x withdraws £25 each week so
1st - £25 withdrawn - leaving £75
8th- £25 withdrawn- leaving £50 and so on.
is there a forumlae for calculating how much interest x will receive in a year?

albertross_2

X's account would be empty by the 22nd of the month..

The answer is about £1.13 (higher rate)-£1.51 (std rate) after tax, if those are intended figures, it's not worth the effort.

The easiest way to look at it is what is the average amount in the bank over the period * 0.05 *0.8 (or 0.6 for higher rate tax payers)

Someone on the savers board may have a mathematically correct formula for you, but this is close..

you will earn interest each month :

25 for 1 day
25 pounds for 8 days
25 pounds for 15 days
25 pounds for 22 days

25 pounds for 46 days * 12 = 552

So the average amount in your account over the year is

25 * 46 / 30.416666 = 37.80

37.80 * 0.05 = £1.89 gross or 1.51 or 1.13 after tax

This is a gross simplification, because it depends on the exact terms of the account, days in each month etc. but gives you a ballpark figure. It might vary by a penny or two due to compounding.

So if n is the amount per month of the initial deposit
taxrate = 0.8 or 0.6 (std/higher rate)
i = 5 (interest rate)

netaninterest = (n/4) * (46/30.41666) * (i/100) * taxrate