Math Problem - help
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15-01-2016, 01:12 PM
RE: Math Problem - help
(15-01-2016 12:43 PM)Full Circle Wrote:  The question I’m trying to answer is:

If I had a total of $100 to invest in these two positions how should I spilt the money up so that in the end they are worth the same (assuming return is static in a finite period).

You didn't specify that in your first post!
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15-01-2016, 01:21 PM
RE: Math Problem - help
(15-01-2016 06:59 AM)Full Circle Wrote:  I thought I would be able to easily work out this algebra problem but alas no.

Two investments. One gains 35% and the other 25%.

How much do I invest in each so that at the end of one year they both arrive at the same dollar gain?

(15-01-2016 12:43 PM)Full Circle Wrote:  The question I’m trying to answer is:

If I had a total of $100 to invest in these two positions how should I split the money up so that in the end they are worth the same (assuming return is static in a finite period).

These are two different problems.
Your first problem seeks to have the gain as the same i.e. 0.35x = 0.25y whereas your second problem seeks to have the total amount the same i.e. 1.35x = 1.25y

If we are solving for y then
in the first problem y = 0.35/0.25 = 1.4x
But in the second problem y = 1.35/1.25 = 1.08x

It seems you have a second equation where x + y = 100
So substitute y from your first equation (I'm not sure if you are using problem 1 or problem 2)
For problem 1
y = 1.4x
x + y = 100
So
x +1.4x = 100
2.4 x = 100
x = 100/2.4
x = 41 + 2/3rds
which means that y = 58 + 1/3rd

For problem 2
y= 1.08x
x + y = 100
So
x +1.08x = 100
2.08x = 100
x = 100/2.08
x = 48.07692
which means that y = 51.92308

Anyway, I'm not sure if you have expressed your problem sufficiently.
Neither of these problems resolves to an answer that can be expressed sufficiently in terms of dollars and cents, problem 1 you need fractions in your answer as you can't express 1/3 as an exact decimal. Problem 2 you end up with decimal points smaller than what can be represented by cents.

But anyway, I hope you can follow the workings and know how to apply this yourself (I think you can because your OP shows that you can). And hope you can understand why problem 1 is different from problem 2.
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15-01-2016, 01:24 PM
RE: Math Problem - help
(15-01-2016 01:12 PM)unfogged Wrote:  
(15-01-2016 12:43 PM)Full Circle Wrote:  The question I’m trying to answer is:

If I had a total of $100 to invest in these two positions how should I spilt the money up so that in the end they are worth the same (assuming return is static in a finite period).

You didn't specify that in your first post!
Facepalm

The problem could still have been solved, though. Just say x+y=z for the second equation, solve simultaneously, and you will get x and y as percentages of z (which is what he was looking for anyway). I didn't see this until he gave a specific number for z (100), but it still works without a specific number.
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15-01-2016, 03:05 PM
RE: Math Problem - help
(15-01-2016 12:39 PM)Full Circle Wrote:  
(15-01-2016 08:57 AM)Chas Wrote:  I will tell you the answer if you tell me what those investments are. Consider

LOL sure.

Had you invested $100 in the Exchange Traded Fund TLT (Long Term Treasuries) in 2008 they would have gained 38% as of today, and that is not including dividends.

Had you invested $100 in the ETF IEF (7-10 Year Treasuries) in 2008 the investment would be up about 27% as of today, not including dividends.

Both positions are up again today in Wall Street’s meltdown going on as I write this.

TLT is more volatile but highly uncorrelated to equities, so when stocks are down it is usually up, the same with IEF to a lesser extent in both volatility and correlation.

Lucky you, the ETF I'm invested in has been hammered, it's a fucking travesty what's going on in my 401K. Fuck Fuck Fuck!!

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20-03-2016, 01:34 AM (This post was last modified: 20-03-2016 01:47 AM by Carlo_The_Bugsmasher_Driver.)
RE: Math Problem - help
(15-01-2016 06:59 AM)Full Circle Wrote:  I thought I would be able to easily work out this algebra problem but alas no.

Two investments. One gains 35% and the other 25%.

How much do I invest in each so that at the end of one year they both arrive at the same dollar gain?

I think I have to solve for two variables simultaneously.


*My feeble attempt so far:

(x)(1.35) = (y)(1.25)

(x)(1.35)/(1.25) = y

(x)(1.08) = y

&

(y)(1.25)/(1.35) = x

(y)(0.926) = x

so then

(y)(0.926) = 0.5
y = 0.5/0.926
y = 0.54

(x)(1.08) = 0.5
x = 0.5/1.08
x = 0.46

but when I plug in

(0.46)(1.35) = (0.54)(1.25)
0.621 =/= 0.675

Arrrggggghhhhhh

help

Brute force shows me that

(0.48)(1.35) = (0.52)(1.25) is much closer
0.648 = 0.65


Weeping

I dunno what equations you're using here, but I'd guess for a basic algebra we're using the compounding interest equation

I = p(1+r/n)^nt

In this case, and assuming the interest is only compounded once in a single year, there are multiple values which would satisfy this arrangement provided that the first principle is 92.59% the size of the second principle

P1/P2 = 0.9259

Unfortunately there is one equation and two unknowns so it cannot be solved for a single value.

I think you left out some critical information.

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20-03-2016, 09:44 AM
RE: Math Problem - help
Pardon me a moment while I think about this.....

X x 35% = z
Y x 25% = z
let z = $385 (for example)

now 385/(35/100) = X
and 385/(25/100) = Y

so X = $1,100
and Y = $1,540

This is only one example that would work as you propose; there are numerous others.

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