I need to construct a model to do the following.

Assume there is a capital amount of £51,000
This needs to be compounded at 5% per annum.
How much can be withdrawn a month to deplete the capital in 25 years (300 months)?

Any ideas anyone? (My maths isn’t that strong!) 😳

I’d use a spreadsheet, I don’t think there’s an easier way.

is the interest applied to the capital sum annually, monthly or daily?

say we took £5k out int he first year would the 5% be paid on £45k or on the average capital available over the course of the year (£47.5k)?

‘interest’ is applied daily though for the sake of the exercise it could be monthly

have a look at this article http://triviasofsubstance.blogspot.com/2007/11/crystal-ball-that-predicts-your-first.html

for the interest side of things accruing daily.

I get £298.64 using monthly interest, with £1 or so left at the end.

Thanks all.

@cynic-al how did you get there?

Spreadsheet!

I just worked out what was in the account at the end of the first month, withdrew, calculated for the second month, withdrw, and so on. Formula was (£51,000-x)*(1.004166666). I then altered the monthly withdrawal until I got close to 0 at the end.

I used 299 months, Maybe I should have used 300, I may well have made a basic error somewhere too.

I reckon that it’s £298.14 per month. Assuming interest paid monthly.

Edit – cynic-al beat me.

Edit again – this was using a spreadsheet.

That’s not maths.

Sure but it’s fun.

Thanks again!

Prepares to look clever in front of client! 🙄 😉

Or another answer:

((£51,000/2)*1.05^25)/300 = £287.84

That’s not monthly 😛

EDIT ((£51,000/2)*1.00416666^300)/300 = £287.84 ❓

so then if i have a cash pot of 250k at retirement and i want 1500 a month how long will it last.. assuming 5% calcilated daily etc..

23.75 years

cheers mefty so thats me hanging it out to dry in 7 years time .. bingo!!

For the OP shouldn’t the monthly interest should compound to give 5% – so that’s 0.4074% per month rather than a flat split of 5/12%=0.4166 per month.

@thepurist You could be right there.

I make it 5/12 = .4166% but as I said…my maths…….

slowjo – it’s 1.05^(1/12) = 1.004074
ie 0.4074% per month.

RealMan – Member
That’s not maths.

And you’re not a Real Man™…yet we allow you to keep on posting.

RM what is it then History? Biology?
It has numbers you work something out with them therefore it is maths

Arguable, surely.

And it’s accounting.

It is a branch of applied maths, accounting does not cope with compound interest particularly well.

I had expected this to turn into an argument of results/methods, instead it’s become an argument on what counts as maths, excellent! 😀

I asked a maths graduate about compound interest. He wrote it down in sigma notation but that was as far as it got. Spreadsheet ftw.

Theoretically is it not discrete integral calculus?

, no need for sigma notation, just a simple equation.

Derived how?

Polynomials, but you don’t need to derive the formula to use it do you. I generally do this stuff on a calculator – albeit a financial one – unless I need to be precise on day count or need to incorporate the yield curve.

No, you don’t need to know how it’s derived, but I’m curious…

It is a branch of applied maths

So is everything. Finance then maybe?