Money maths - how good are you? Poll discussion

Mics_chick

The answer is C

wisp_2

not sure I'd bother with the stock exchange with just 100 quid - be better to overpay the mortgage with it - definately saving small amounts of interest for the next 25 years...

wisp:j

kennyboy66_2

King_Weasel wrote: »

So many numbers!

I hope the mathematicians didn't have to get out their spreadsheets to answer this one.

There are two elementary arithmetical principles here that tell us, FIRST, that the values of A and B must be equal and, SECONDLY, that the value of A and B must be less than the value of C. (And the logicians wll tell us that you don't need the first principle to arrive at the answer if you use the second principle twice.)

FIRST PRINCIPLE: which is bigger - 7 x 6 or 6 x 7 ? You don't need to know your times tables to answer this: you can multiply numbers in any order you like without altering the result. The value of A is your original investment - say, £100 - times 1.05 ^ 4 (or 1.05 x 1.05 x 1.05 x 1.05) and then times 0.95 ^ 4. The value of B is £100 times 0.95 ^ 4 then times 1.05 ^ 4. These answers must be the same.

SECOND PRINCIPLE: which is bigger - 10% of £10 or 10% of £20? (Again, you don't need to know what 10% of £10 or £20 actually is.) This is basically what alexjohnson was trying to tell us. I think he's right. So if you add a percentage - 5%, in this case - to your original investment and then deduct the SAME percentage off your new and higher value you are bound to finish up with less. (Take an extreme example if it helps: try increasing your investment by 100% and then reducing it by 100%.) So £100 x 1.05 x 0.95 must be less than £100. And of course you get the same result if you knock the 5% off first and then add it back, as in situation B.

If you can't follow this, get your spreadsheet out after all. You will get an answer, but may not know why.

A beautiful explanation.

Former_MSE_Archna

Poll Title: Poll started 22 May 2007. Money maths - how good are you? This is a repeat of a poll I did back in 2005, to see how good you are at figuring out a basic, but not straightforward money sum. Which of the following gives the best return? (correct answer in next week's e-mail) The stockmarket....

A. rises 5% a year for 4 years then drops 5% a year for 4 years
32.2% (1786 Votes)
C. stays the same
28.3% (1572 Votes)
D. all are equal
25.3% (1408 Votes)
B. drops 5% a year for 4 years then rises 5% a year for 4 years
13.9% (776 Votes)

Total Votes: 5546

P.S. The correct answer is C!

MSE_Martin

The answer is C.

I was going to write a long explanation about the commutative nature of maths and the fact that 25% off a value always had a bigger impact than 25% added to a value.

Yet as King Weasel has done it so well above I thought I would simply use his...

"So many numbers!

I hope the mathematicians didn't have to get out their spreadsheets to answer this one.

There are two elementary arithmetical principles here that tell us, FIRST, that the values of A and B must be equal and, SECONDLY, that the value of A and B must be less than the value of C. (And the logicians wll tell us that you don't need the first principle to arrive at the answer if you use the second principle twice.)

• FIRST PRINCIPLE: which is bigger - 7 x 6 or 6 x 7 ? You don't need to know your times tables to answer this: you can multiply numbers in any order you like without altering the result. The value of A is your original investment - say, £100 - times 1.05 ^ 4 (or 1.05 x 1.05 x 1.05 x 1.05) and then times 0.95 ^ 4. The value of B is £100 times 0.95 ^ 4 then times 1.05 ^ 4. These answers must be the same.
• SECOND PRINCIPLE: which is bigger - 10% of £10 or 10% of £20? (Again, you don't need to know what 10% of £10 or £20 actually is.) This is basically what alexjohnson was trying to tell us. I think he's right. So if you add a percentage - 5%, in this case - to your original investment and then deduct the SAME percentage off your new and higher value you are bound to finish up with less. (Take an extreme example if it helps: try increasing your investment by 100% and then reducing it by 100%.) So £100 x 1.05 x 0.95 must be less than £100. And of course you get the same result if you knock the 5% off first and then add it back, as in situation B.

If you can't follow this, get your spreadsheet out after all. You will get an answer, but may not know why."



For those who simply want a numerical answer, here it is:

• Option A. Rises 5%/year for 4 years then drops 5%/year for 4 years. END RESULT: 99% of the start value
• Option B. falls 5%/year for 4 years then rises 5%/year for 4 years. END RESULT: 99% of the start value
• Option C. Stays the same. END RESULT: 100% of the start value
• Option D. All of the above. NOT TRUE AS A, B & C produce different answers.

The fact so few people got this right (as in 2005) shows the worry about how financial marketeers use maths to confuse!

Martin

Princess_Jane

I've got dyscalculia, which is the sort of the numerical form of dyslexsia, so there is no way I could work this out in a month of Sundays.

I have to carry a calculator everywhere and struggle to do change from a pound.

Hats off to everyone who worked it out!

webwiz

alexjohnson wrote: »

Martin and Lawrence,

What is rattling around in my head about this is the prejudice I detect against stocks in this example. My tounge is almost completely in cheek - but only almost. It really does bother me that you always push cash ISA's, because you're smart and people listen to you. I assume this is because anything else is a regulatory minefield and you don't want to go there, which is fair enough.

But over the long run, cash will perform more poorly than stocks (let's not go into the academics of it, and I think the statement is a fair one). ISA's are supposed to be about long term saving. Horse for courses - some people want to sleep easily at night. Some people are saving for something like a house deposit and want to know that the money is there. But I do wish you would ask people who are maxing out their cash ISA entitlement and who are saving for a rainy day at least to think about a low cost tracker, or taking some advice. I know it is in the articles, but you talk about it for stoozing, for example. Should you put a stooze pot in the stock market? Well that's not for me to decide but that is very risky. But by maxing out an ISA with a stooze pot (money borrowed from a credit card at 0%), you are capping your tax-free return at around 5.5%. That seems penny-wise and pound-foolish to me. But hey - your site, your rules!

I agree that equities will (or at least always have) outperform cash in the long run. But everyone should have some cash in their portfolio for "rainy days". So the question is: should people use their ISA allowance for cash + shares in minis or all in shares in a maxi. The answer is clear for most people. The point of an ISA is that it is a tax free wrapper, but most people will not get any tax advantage from a shares ISA as there is no longer any tax relief on dividends and few people will exceed their tax free capital gain allowance. So a cash ISA is the first port of call.