Can you figure it out?

Former_MSE_Andrea

Poll Title: Poll started 26 April 2005. Can you figure it out? This isn't an opinion poll, but a test to see how many people can figure out some basic, but not straightforward money sums. Which of the following gives the best return? The stockmarket....

a. rises 10% a year for 5 years then drops 10% a year for 5 years
b. drops 10% a year for 5 years then rises 10% a year for 5 years
c. stays the same
d. all are equal

Vote or click reply to discuss

divadee

i think a but then maths was never my strong point. and i have done this in my head, so dont all laugh when im wrong.

flea72

i say C, but im not too sure why

the first two, make me think of percentage of percentages, if that makes sense, which means they dont increase and decrease in equal amounts, so you cant get back to your starting point, which rules out the D answer too?

mink35

Well the first two would give you a loss after 10 years so I would say C - it won't have made money but it won't have lost either like the first two.

On the other hand you should have put ya money in an ISA and then you'd be quids in!

HLK

C for me. Still thinking about why but you end up with less than you started with for the first two.

mmmm.... maybe that's why endowments hit the skids!

40079

Spreadsheets are great for "cheating" on this sort of question. What I'm struggling to rationalise how both a and b come to the same (lower) answer, therefore c is best.

If the stockmarket rose and fell in alternate years by 10% or fell and rose by 10% you also get to the same answer!!

StephenB_2

The non-numerical reason is that the 10% fall is always from a bigger number than the 10% increase, and 10% of a bigger number (the fall) is bigger than 10% of a smaller number (the increase). Try it with 100% instead of 10%.

NUmerically, a 10% increase is the same as multiplying by 1.1. A 10% decrease is the same as multiplying by 0.9. So a 10% increase followed by a 10% decrease is the same as multiplying by both, ie 1.1 x 0.9, which is 0.99. So any combination of 5 years-worth of 10% increase and 5 years-worth of 10% decrease is going to arrive at 0.99 x 0.99 x 0.99 x 0.99 x 0.99, which is certainly less than one, and turns out to be 0.951.

So options (a) and (b) are the same, and option (c) is better.

Easy!

SJB

robnye

c) cos the simplest things in life dont change........ ;-)

Debbie_Hobdell

Maths isn't my best subject either, I sat down with pen & paper, but if I've done it right, then C) is the best option.

A) actually comes out ever so slightly worse off than - but don't quite me on that!!!

Debbie_Hobdell

Hety, how come there's a signature at the end of my post which is nothing to do with me?!

jjay_3

A)

Start with £100
After 1 year: £110 (+10%)
After 2 years: £121 (+10%)
After 3 years: £133.10 (+10%)
After 4 years: £146.41 (+10%)
After 5 years: £161.05 (+10%)
After 6 years: £144.95 (-10%)
After 7 years: £130.45 (-10%)
After 8 years: £117.41 (-10%)
After 9 years: £105.67 (-10%)
After 10 years: £95.10 (-10%)



Start with £100
After 1 year: £90 (-10%)
After 2 years: £81 (-10%)
After 3 years: £72.90 (-10%)
After 4 years: £65.61 (-10%)
After 5 years: £59.05 (-10%)
After 6 years: £64.95 (+10%)
After 7 years: £71.45 (+10%)
After 8 years: £78.59 (+10%)
After 9 years: £86.45 (+10%)
After 10 years: £95.10 (+10%)

C)

Start with £100 and end with £100

D)

All are NOT equal

C gives you the best return. Unless my sums are wrong.....