Can you help me with this calculation?

EddScott

EddScott

EddScott

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A payment of £100 per month over 25 years is a total of £30,000


There is a figure of £507,000 at a growth rate of 8.5%

Is there any way of calculating how much the £100 per month should increase every year to provide the figure of £507,000 at 8.5%?

In the form of a % ?
 
Thanks for the links.

My problem is that I'm not trying to work out how much the monthly premiums need to be to get to £507,000. I need to work out by how much the £100 should increase every year to be able to provide the investment enough input to reach £507,000 if the investment grew at 8.5% compound.

I think its around the £65,000 mark. But I'm not sure by what percentage that should have been to increase the £100 a month - the total contribution over the term was £30,000 - it should have been around £65,000. About 5.5%???

I'll see if I can get my head round the formula and try and work it out. Apparently the actuaries of a well known high street bank that didn't fall foul of the crunch cant work it out!
 
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I'm not quite clear what you're asking. Is it:

How much money do I have to invest every month so that I'd make £507,000 after 25 years at 8.5% annual return?

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Edit:

An actuary will be able to work this out if you're phrasing the problem right. At the moment you seem to be a bit confused as to what you want.

If you invest £100 per month at 8.5% interest per year continuously compounded, you'll get around £100,000 after 25 years.

If you want to make £507,000 after 25 years at 8.5% interest, you need to be investing around £500 / month.
 
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That sounds horribly like some sort of differentiation exercise....

Basically you have the start point (£1200 per annum), the interest rate (8.5%) and the total you want to achieve (£507,000).

So the figure you're looking for is several points along the line between the start point and end point, and then the difference between what that point would be if calculated from start and interest, and what it needs to be to hit the target, and that is your increase amount.

You could solve it graphically, it would be the area between the two lines if you graphed both sets of compounded data. My maths is far too rusty to work out the equation for it tonight though.
 
Hmm, I think I understand now.

You're saying that for the first year you put in 100/month (so 1200 for the year).

In the second year you put in 1200 + X

In the third year you put in 1200 + X + X, etc.

Each year you get 8.5% interest, and you want to know what X is so that after 25 years you have £507,000?

If that's the case, then if we let r be your rate of return (8.5%), A be your initial yearly investment (1200) and N be the number of years you invest (25) and P(N) be the value of your investment after N years, then

P(N) = (Ar + X) [(1+r)^N - 1] / r^2

and you need to invert that to give X, knowing that P(25) = 507,000:

X = P(25) r^2 / [(1+r)^25 - 1] - Ar

X = 507000 * (0.085)^2 / [(1 + 0.085)^N - 1] - 1200 * 0.085

X = £445.80

What you really need is the figure X/12 = £37.15, so:

In year 1 you invest £100 / month
In year 2 you invest £137.15 / month
In year 3 you invest £174.30 / month

etc

Actually, now I typed that out I realize that I calculated this assuming you were increasing your investment linearly every year, which is clearly unrealistic. Oh well, it was still interesting.

I'm going for a run now. When I get back I might redo the calculation for a geometric increase in your annual investment.

Actuaries can go suck my balls.
 
Roubini - I think thats it - but it doesn't have to get to £507,000. - When I write to the Ombudsman I want to use formula to prove a point and make it look like I know what I'm talking on about :)

I'll explain a bit more. I'm dealing with a complaint regarding a pension.

In 1990 person A was told that if they invest £100 for 25 years at the end they would have £507,000 IF the investment grew by 8.5%.

Pension illustrations around that time made (hugely unrealistic) assumptions that your wages (and therefore your contribution) would increase.

The mistake is that there was no mention of these assumptions - there is obviously an assumption that the £100 will increase every year.

The end figure doesn't have to be £507,000 - the rate I'm looking for is by what rate the £100 needs to grow every year to POTENTIALLY produce a growth rate of 8.5%.

Theres also one caveat that the rate of increase in the monthly/annual payment can't be higher than the 8.5%. That was a rule of the time.

I can't ask for the £507,000 because fund performance is guesswork and we no the "no guide to the future" cobblers. What I'm asking for is the money that should have been invested over the period in order to POTENTIALLY provide £507,000 IF it grew at 8.5%.

Simple really.


EDIT - check this out. http://www.actuaries.org.uk/sites/all/files/documents/pdf/illustrations.pdf

Pages 39 and 40. Shows intial payments of just over £100 and at 8.5% the fund is £497,000. On page 40 it states the assumption of the salary increase from £16K to £111K.

Its the assumption of the rate of salary increase I'm after.
 
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EddScott said:
Pages 39 and 40. Shows intial payments of just over £100 and at 8.5% the fund is £497,000. On page 40 it states the assumption of the salary increase from £16K to £111K.

Its the assumption of the rate of salary increase I'm after.
Click to expand...
Rate of increase per... month? Year? Per year it's a 8.056% salary increase to go from £16k to £111k over 25 years.

EDIT: As the calculation is 16(x^25)=111, where x is the rate of salary increase (to the power of 25 because it's 25 compound increases). Rearrange to have x^25 = 111/16, then x = 25th root of(111/16), which is 1.08056.

EDIT2: It might be x^24 if your salary increases are considered at the end of the year (which would make sense, as you wouldn't get a pay rise on day 0), as your "final" pay rise only starts being realised after the term has expired. In that case it's 1.084 i.e. 8.4%.
 
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