Money Quiz: Can you work it out? Poll results/discussion

Schamansky

Phil wrote: »

a) 95.099%
b) 95.099%
c) 100.00%

I went for D after trying to work it out in my head but actually it's C, isn't it...?

Got the same result putting 10000£ into Excel and letting them rise/fall, respectively fall/rise, at 10%. The result, £9509.90, is the same in both cases, at a 5% roughly.

Then figures don't lie; now someone tell me why. Because my mind keeps telling me that it shouldn't be like that and you should come out at 10k again either way round. Well, obviously not. But why? Geometrical progression and stuff...don't know.

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Right, here's my shot. Mathematicians, get ready to crush me.


Let SA be the starting amount and BL the bottom line figure after 10 years.

Scenario A) BL = SA * 1.1^5 * 0.9^5 rise first, then fall
Scenario BL = SA * 0.9^5 * 1.1^5 fall first, then rise

With A or B, it does not matter in which order the rise or fall occur, due to the law of commutativity in multiplication. The result will be identical either way.

Hence for both scenarios BL = SA * 0.95099

The factor 1.1^5*0.9^5 = 0.95099 gives us the end amount of roughly 95% of any original investment. Since the factor is <1 , it's wiser to leave the money under the mattress, in which case that factor would be 1, same in, same out (at zero inflation).

Scenario C) BL = SA (money under the mattress)

So better off (no gain, no loss) with C.

teddyco

Jimmythewig,

You are right, anything is better than a garden variety savings account.

McSaver

The answers I. The Icesave savings accounts

Dorrie

Answer is C (not sure why some of you had to use a calculator though!)

bigpat

Answer is C

A&B are the same as each other and leave you over 1% off

English_Bob

This is the exact reason that we all need to be careful when dealing in percentages.

JimmyTheWig

Schamansky wrote: »

Then figures don't lie; now someone tell me why. Because my mind keeps telling me that it shouldn't be like that and you should come out at 10k again either way round.

Forget about all the years, that just adds complication. Shrink the problem to one year it goes down, the next year it goes up.
Lets make things even easier to understand and rather than a 10% change lets consider a 50% change.

Now, if you start with £100 and it goes down by 50% you have £50. If that goes up by 50% then you have £75. So you have lost out. (And the same would be true in the other order.)

The answer is that the inverse of +x% is not -x%.
+x% means multiply by (1+x/100). The inverse of this, then, is to divide by (1+x/100).

johncolescarr

An interesting argument, but has the market ever performed in this way?

I am new to this sort of thing, but isnt it the case that over time the value of the stock market, say FTSE100 has always increased at a greater rate than if the money was in a savings account, obviously with peaks/troughs. Therefore the value of your investment would only be less is you were to cash in your investments after 10 years rather than wait for a market recovery? Obviously if you have a fixed term investment, you'd be stuck!!

JimmyTheWig

johncolescarr wrote: »

An interesting argument, but has the market ever performed in this way?

I am new to this sort of thing, but isnt it the case that over time the value of the stock market, say FTSE100 has always increased at a greater rate than if the money was in a savings account, obviously with peaks/troughs. Therefore the value of your investment would only be less is you were to cash in your investments after 10 years rather than wait for a market recovery? Obviously if you have a fixed term investment, you'd be stuck!!

Has it performed exactly like this? I would be very surprised!
Have there been peaks and troughs? Yes, most certainly.
Have there been times when it is down to 95% of its former value. Yes.

I believe that the point of the question is to demonstrate the way percentages work and to be wary of risky investments.

I completely agree, though, (as per my earlier post) that over the long term the stock market should out-perform savings accounts.
So how about if the question were stock market rises by 20% a year for 5 years then stagnates (i.e. 0% rise) for 5 years vs stock market rises by 10% a year for 10 years?
I think this proves the same point whilst accepting ultimate growth.

cal

The key in understanding is in the use of multipliers.
p% inc means multiply by 1 +decimal equivalent
p% dec means multiply by 1 - decimal equivalent
Hence inc by 10% dec by 10% means x1.1x0.9, the nature of multiplication means order does not matter so £100 becomes £90 becomes £99
OR £100 becomes £110 becomes £99.
To cope with working in head (or doing it in the street) always say what if it was £100 and then test it!!