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Original poster

Any mathemeticians out there?

42 replies

moonstone1201 · 23/08/2007 21:27

Ok this is a bit of a weird one, but I'm hoping to have it solved by the time I get to work tomorrow.

If someone has £x and invests this at a rate of 5% per year, taking an income starting at £9607, which increases by 5% per year for 15 years, how much does x need to be to run the fund down to zero within this time?

I've looked all over the web for a calculator to work this out but I'm not even sure what I'm searching for. Pension calculators seem to be the closest thing, but none of them seem to allow for the increasing income.

Any help appreciated!

OP posts:
Kathyis6incheshigh · 23/08/2007 21:30

have set dh to work with a pencil and paper (he is mathematician) to solve it for you, may take a few mins

Kathyis6incheshigh · 23/08/2007 21:44

take the income you want (9607), multiply by number of years (15), divide by 1.05

you get £137242.86(ish)

he is v knackered though so he has probably missed something here - seems a bit too easy

CantSleepWontSleep · 23/08/2007 21:48

No, she wants the income to increase by 5% each year, not stay fixed at 9607.

Will have a quick go myself, but am also v knackered!!

SlightlyMadStar · 23/08/2007 21:49

Mmmm,

I didn't think it was quite that simple - as I recall from my A level maths.....I thought you needed to do geomettric series and silly stuff like that (which is why I ignored the question int eh first place..)

SlightlyMadStar · 23/08/2007 21:50

I have my calculator out too....

ChasingSquirrels · 23/08/2007 21:50

easy excel s/sheet (cant be arsed doing the algebra), but excel is on the pc and I'm on the laptop, will go and work it out and see if I get the same no as csws

SlightlyMadStar · 23/08/2007 21:53

OK - over 15 years your total income will be £195,652.84.

Are you taking the income at the same time as the investment at 5% starts?

SlightlyMadStar · 23/08/2007 21:54

I just used excel actually.

Or is the investment phase complete before taking an income?

ChasingSquirrels · 23/08/2007 21:54

was just wondering that SMS, but wondered if it was slightly picky - lol

Kathyis6incheshigh · 23/08/2007 21:54

OK just asked him and he showed me a big page of calculations by which he arrived at that - apparently it is a first order difference equation with a resonant forcing term. The thing I gave you as the way to work it out is the solution he arrived at via lots of complicated stuff.
(I don't understand any of this btw.) So, yes, it does take into account the income increasing.

Kathyis6incheshigh · 23/08/2007 21:55

he is interested to know why you want to know!

ChasingSquirrels · 23/08/2007 21:57

no, actually what I wanted to know was whether you drew the income at the start or end of the year (am not factoring in a monthly income)

SlightlyMadStar · 23/08/2007 21:57

My dodgy maths thinks you need more than £100K to start.

SlightlyMadStar · 23/08/2007 22:01

£127K investment is my current answer.....

ChasingSquirrels · 23/08/2007 22:01

yup - as per kathy's dh, and still haven't done the algebra but the explanation sounds right aswell.

SlightlyMadStar · 23/08/2007 22:02

vut £127 would change a bit dependant when in the year income was taken out and interest added, and income increased etc.

SlightlyMadStar · 23/08/2007 22:03

But Kathys Dh doesnmn't take into account increasing income...

Kathyis6incheshigh · 23/08/2007 22:04

Yes he does SMS.
The solution I've given you is arrived at via a page of calculations. Honest!

CantSleepWontSleep · 23/08/2007 22:04

My head hurts because I'm trying to remember the proper way to work it out, rather than just banging the numbers into a spreadsheet (see, that's the mathematician in me coming out!). Unfortunately I am no longer a good mathematician, and I'm admitting defeat!

It's going to bug me now though - how do you properly work out

Sigma 1.05 to the power of n from n=0 to n=14 (that would look so much nicer if we had the right options on the keyboard!)

SlightlyMadStar · 23/08/2007 22:07

Yes Sigma is def involved but I can't remember either and don't have my stats calculator at home to do it.

SlightlyMadStar · 23/08/2007 22:07

These are the incomes I have calculated:

1 9067
2 9520.35
3 9996.3675
4 10496.18588
5 11020.99517
6 11572.04493
7 12150. 64717
8 12758.17953
9 13396.08851
10 14065.89293
11 14769.18758
12 15507.64696
13 16283.02931
14 17097.18077
15 17952.03981

They all add up to £195652.84

ChasingSquirrels · 23/08/2007 22:08

kathy's dh is definately right and does take into account increaseing income, the only variable is when the income is taken (Kathy's dh's calc is assuming it is taken at the end of the year after the capital has grown by 5%), it would in all probability be taken monthly, but it won't affect x that much.

csws - I haven't even attemted the algebra, it's all tooo long ago

ChasingSquirrels · 23/08/2007 22:10

9607 not 9067

Kathyis6incheshigh · 23/08/2007 22:14

CS - yes, he has assumed that. He says provided the interest on the capital and the rate of increase of the income are compounded in the same way the solution is correct.
Where he said 1.05 you should take the AER.

(this is all gobbledigook to me )

Kathyis6incheshigh · 23/08/2007 22:15

God you people are clever