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    • MSE Martin
    • By MSE Martin 3rd Sep 13, 7:50 PM
    • 8,094 Posts
    • 42,221 Thanks
    MSE Martin
    • #2
    • 3rd Sep 13, 7:50 PM
    • #2
    • 3rd Sep 13, 7:50 PM
    Here's my quick explanation:
    Spoiler (highlight below to view):


    The answer is C. The market stays the same.
    First let me give you the numerical answer:

    Option A. Rises 10%/year for 4 years then drops 10%/year for 4 years. END RESULT: 96% of the start value.
    Option B. Falls 10%/year for 4 years then rises 10%/year for 4 years. END RESULT: 96% of the start value.
    Option C. The market stays the same. END RESULT: 100% of the start value.
    Option D. All the above answers are equal. NOT TRUE AS A, B & C produce different answers.

    Now on to why:

    The most important thing to understand is that if you add X% on a value then take X% off – you'll always end up with less than you started with.

    If algebra is confusing lets try again this time with an example. You have £100 and get 20% on it. Now you've £120, but then you take 20% off that and (as 20% of £120 is £24) you've only £96 left.

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

    And this is commutative (it works both ways round) so let's do it the other way. You start with 100 and take 20% off, now you've £80, then you add 20% to £80 and you get £96. This is because again you're adding the 20% to a smaller number than you're taking it off.

    Hope that helps. If you're not sure try it on a calculator yourself.




    Click reply to discuss
    Last edited by MSE Martin; 03-09-2013 at 7:53 PM.
    Martin Lewis, Money Saving Expert.
    Please note, answers don't constitute financial advice, it is based on generalised journalistic research. Always ensure any decision is made with regards to your own individual circumstance.

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    • bsms1147
    • By bsms1147 3rd Sep 13, 7:56 PM
    • 1,866 Posts
    • 3,285 Thanks
    bsms1147
    • #3
    • 3rd Sep 13, 7:56 PM
    • #3
    • 3rd Sep 13, 7:56 PM
    Well played, Martin, well played.

    I got the right answer but had to maths my way there. Quite counter-intuitive until you explain it like you did.
    • Kaz2904
    • By Kaz2904 3rd Sep 13, 7:56 PM
    • 5,793 Posts
    • 37,611 Thanks
    Kaz2904
    • #4
    • 3rd Sep 13, 7:56 PM
    • #4
    • 3rd Sep 13, 7:56 PM
    Oh. I was wrong then!
    Debt: 16/04/2007:TOTAL DEBT £92727.75 £49395.47 £43332.28 repaid 100.77% of £43000 target.
    MFiT T2: Debt £52856.59 £6316.14 £46540.45 repaid 101.17% of £46000 target.

    2013 Target: completely clear my £6316.14 £0 mortgage debt. £6316.14 100% repaid.
  • Gabs27
    • #5
    • 3rd Sep 13, 7:56 PM
    • #5
    • 3rd Sep 13, 7:56 PM
    I voted C
    as using 1 as a base figure A and B give a result of 0.96 whereas C give 1
    • Comyface
    • By Comyface 3rd Sep 13, 7:59 PM
    • 628 Posts
    • 540 Thanks
    Comyface
    • #6
    • 3rd Sep 13, 7:59 PM
    • #6
    • 3rd Sep 13, 7:59 PM
    I got there working it out without numbers, kind-of like you explained. Wouldn't have been surprised if I'd been wrong, though.

    Liked giving my rusty-maths brain a workout
    Are the words 'I have a cunning plan' marching with ill-deserved confidence in the direction of this conversation?
  • b e a r
    • #7
    • 3rd Sep 13, 8:00 PM
    • #7
    • 3rd Sep 13, 8:00 PM
    I had to do a small bit of work in Excel to get the answer and was surprised. I realised that if the amount is changing then the amount of the 10% is changing and that will have an effect. I expected this to result in a higher result. Having done the maths it does make sense.
    Will give this to some of my more able year 6 pupils near the end of the year and see what they think.
    • zagfles
    • By zagfles 3rd Sep 13, 8:17 PM
    • 10,692 Posts
    • 8,796 Thanks
    zagfles
    • #8
    • 3rd Sep 13, 8:17 PM
    • #8
    • 3rd Sep 13, 8:17 PM
    If you can do a bit of simple algebra it's obvious really:

    (1+x)*(1-x) = 1-x^2

    It's even more obvious if you use 100% instead of 10%
  • dgwebster
    • #9
    • 3rd Sep 13, 8:20 PM
    • #9
    • 3rd Sep 13, 8:20 PM
    Whoop whoop. Instinctively got the right answer straight away, but my job is massively statistical anyway so would have been an embarressment to have gotten it wrong.
    • FattyBettyBoo
    • By FattyBettyBoo 3rd Sep 13, 9:09 PM
    • 459 Posts
    • 713 Thanks
    FattyBettyBoo
    I can't highlight the answer on my iPad ... Which was right?
    I seldom end up where I wanted to go, but almost always end up where I need to be

    Debt at present ...
    Halifax (0% July13) - £1,920, BarclayCard (0% Sept13 & Jan14) - £4,260
    • too_much_debt
    • By too_much_debt 3rd Sep 13, 9:18 PM
    • 3,140 Posts
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    too_much_debt
    Yes, I got it right!
    Sealed Pot Challenge #64
    Long Haul Supporter #147
    Nectar Points: 805 = £4.02
    • fat-pudding
    • By fat-pudding 3rd Sep 13, 9:38 PM
    • 155 Posts
    • 52 Thanks
    fat-pudding
    I think you're wrong Martin, as you didn't take into account that if you owned shares then an amount of money would get paid as dividends.

    In *theory* (and in the real world it's slightly more complex) but if you had 4 good years then 4 bad years these early good years might pay more in dividends which gives you 8 years to earn interest on the money. If you also take into account the rate of inflation your holding would be worth less money each year which would again back earning dividends earlier on.
    • Hippipal
    • By Hippipal 3rd Sep 13, 9:44 PM
    • 49 Posts
    • 336 Thanks
    Hippipal
    I got it right, but had to do the maths with an example, rather than knowing why!
  • Jon_k
    Is this an illustration of my theory that, with the exception of MoneySavingExpert, the only people guaranteed to make money from financial advice are financial advisors & of course the bankers!
    • Sharon87
    • By Sharon87 3rd Sep 13, 10:10 PM
    • 3,328 Posts
    • 2,787 Thanks
    Sharon87
    I got it right on my initial thought, but then done an example to confirm it before I submitted.
  • shadeout_mapes
    I think you're wrong Martin, as you didn't take into account that if you owned shares then an amount of money would get paid as dividends.

    In *theory* (and in the real world it's slightly more complex) but if you had 4 good years then 4 bad years these early good years might pay more in dividends which gives you 8 years to earn interest on the money. If you also take into account the rate of inflation your holding would be worth less money each year which would again back earning dividends earlier on.
    Originally posted by fat-pudding
    This is an amusing sum.

    But I think fat-pudding hit the nail on the head. Given that most stocks generate a cash flow, if the P/E ratios remained the same with the price fluctuations, I would always choose higher cash flows initially. Even if re-invested at a modest interest rate, option A will beat option C.

    This question doesn't take into consideration the time value of money.

    But I'm just being difficult now, so let me shut up.
    • Naf
    • By Naf 4th Sep 13, 12:00 AM
    • 2,775 Posts
    • 1,960 Thanks
    Naf
    I can't highlight the answer on my iPad ... Which was right?
    Originally posted by FattyBettyBoo
    Copy & paste it into your notes.
    Answer was C
    Never argue with stupid people, they will drag you down to their level and then beat you with experience.
    - Mark Twain
    Arguing with idiots is like playing chess with a pigeon: no matter how good you are at chess, its just going to knock over the pieces and strut around like its victorious.
    • AlexLK
    • By AlexLK 4th Sep 13, 12:13 AM
    • 4,657 Posts
    • 23,190 Thanks
    AlexLK
    I was correct, nor did I find the problem difficult. *smug*

    £32,000 in debt on 2/9/2013. Debt free on 12/1/2015.
    Saved £11,000 in 2015.
    Savings 2016: £2330.
    Challenge 1 (£500 from decluttering in March): £250
    • yz324
    • By yz324 4th Sep 13, 1:30 AM
    • 74 Posts
    • 8 Thanks
    yz324
    I misunderstood the question...

    I thought the 3rd question mean the first two things are the same. the poll result just shows how badly maths is taught in the UK...
  • ExPat Taff
    Am I being really dim?
    I may be being particularly thick, but surely the time this runs for means that the changes are compounded?

    Rising 4 years and then falling 4 years means you end up with less than you started with (the falls are numerically bigger than the rises were).

    Falling 4 years then rising 4 means the gains are larger.

    In numbers terms:
    Four years rise then four year fall.

    Start with £100.00 in year 1, by year 2 it's x1.1 = £110.00, year 3 £121 and year 4 £133.10; then fall by 10% (i.e x0.9) year 5 £119.79, and so on to give £107.81, £97.03 and then £87.33.

    Four years fall then four year rise.

    Start with £100.00 in year 1, by year 2 it's x0.9 = £90.00, year 3 £81 and year 4 £72.90; then rise by 10% (i.e x1.1) year 5 £80.19, and so on to give £88.21, £97.03 and then £106.73.

    Or like I say, am I being really dim?
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