How good is your money maths?

Disgustified

fozzeh wrote: »

Maths exams always clearly state "Do not use a calculator on this section".

This section did not say this.

You are reading too much into the question.

A: The question is closed ended (it asks you “which of these” and gives you 4 options, nothing else)
B: It gives fixed variables (so does not included external factors in the end outcome, whether they would be applicable in the “real world”)
C: Gives you the option to pick one without looking like a fool.
Whilst A and B can’t be changed, C is always tried to its limits. Jeez Louise!

Next weeks question will be what is 1 plus 1?
Please pipe up with "Well, it would be 2 if you didn’t take RPI and inflation into the equation!"

Thanks for the thumbs down.

I think I must be a bit of a purist, I also draw the line at using my phone during pub quizes.

Can't be sure without a time machine but I also think the answers have changed on the homepage and are no longer identical to those in the first post, which suggests not everyone shares your opinion that some of them weren't ambiguous.

I also think that the point is not to show how clever people are, but actually to demonstrate how clever people are not. If you get the question wrong then read how it actually works out the message is stronger.

People will think "Oh actually not everything in Finance is how it seems, I will look more carefully next time" and also the dicussion which they are engaged in afterwards is supposed to make people feel free to question, instead of staying quiet because they think they might sound stupid or be admonished by someone superior to them.

Empowering people is what MSE is all about.

pjmony

Doh! I'm one of the thickies - I didn't read the question properly.

rpb

For those still confused, it may help to simplify the situation to see what is going on. Just use one year:

Say you have £100 invested, gain 10% in one year and lose 10% in the next.

- In Year 1 you start with £100, and a 10% gain would be £10, so you now have £110 (£100 = £10).
- In Year 2 you start with £110, and a 10% loss would be £11, so you now have £99 (£110 - £11).

These aren't rounding errors here, they are exact. Repeat the process four times and you can probably see how you end up with around £96, losing about a pound each year.

If you do it the other way around you also get an exact answer:

- In Year 1 you start with £100, and a 10% loss would be £10, so you now have £90 (£100 - £10).
- In Year 2 you start with £90, and a 10% gain would be £9, so you now have £99 (£90 + £9).

The reason A and B give the same answer is because, as Martin said, multiplication ("timesing") is commutative, which means it doesn't matter what order you multiply two numbers because the answer is the same (i.e. a x b = b x a, where a and b represent any two numbers).

SacreVert

The reason this works is because you're taking 20% off a bigger number than you're adding 20% too.

Spelling error in the answer. It should be "to" rather than "too".

Sorry to be a pedant but how else can we get the children to write in English.

batvink

I'm going to play devil's advocate and disagree with the official answer.

While the shares are rising 10% year on year, you are highly likely to get dividend payouts. When the shares are stagnant or falling, there is unlikely to be any payout.

Therefore, only option A is likely to result in dividends for the first four years, and they are very likely to amount to more than 4% over 4 years, making it more favourable than B or C.

NSG666

dougz wrote: »

Yes but, if they had made enough taxable capital gains elsewhere, they could offset those profits against the 4 loss years of A or B, thus reducing their tax bill and the net result would be a significant gain in comparison to situation C. If they are wealthier in higher tax band they benefit all the more from this.

Even with your scenario C would still be the better outcome.

Sarita

Wow, now Martins posted his explanation alongside Lees original answer what scares me is that TWICE I misread as being 'the market rises 10% for 4 years, and then rises 10% for 4 years' - even though I thought it was a little odd! Doesn't bode well for my ability to closely read the small print in real life!
Anyway thanks for the explanation...

Heithinn

With "a" it's possible to sell them if they rise by 46% , or drop back to 33% increase, and then buy something else.

Regshoe

Depends on whether you are just holding onto a set stock or buying/selling stock or, options, or selling short/buying long . If you are using options etc. then you will likely want some movement one way or the other!

But the mathematical explanation for the question that is being asked is simply:

final value =a x [(1-b) x (1+b)]^n
=a x [-b^2 +b -b +1]^n
=a x [1-b^2]^n

0<b<1

Where a is the starting investement, 1-b is the increase for the period where the market falls by b (%) and 1+b is the decrease for the period where the market rises. For the given scenario b = 0.1 (or 10% if you prefer) and n =4 (4 matched iterations of increases and decreases). Clearly for any number in the given range the final value will be less than a, as [1-b^2]^n will be less than 1.

happyinflorida

well I'm completely and utterly confused - what is the answer?!!!! There's nothing on the bit where it should be?!!! I know I'm thick at maths but I thought I'd have a go, wish I hadn't now.