Math Problem - help
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15-01-2016, 06:59 AM
Math Problem - help
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 am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
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15-01-2016, 07:01 AM
RE: Math Problem - help
Now you're off into fantasyland.



Show me ANY investment that can guarantee just a 20 percent guaranteed payback, and I'll kiss your ass.....

Wink

.......................................

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15-01-2016, 07:10 AM
RE: Math Problem - help
(15-01-2016 07:01 AM)onlinebiker Wrote:  Now you're off into fantasyland.



Show me ANY investment that can guarantee just a 20 percent guaranteed payback, and I'll kiss your ass.....

Wink

Pucker up baby.

I never said guaranteed. I have two similar investments, over the course of the last seven years one has returned 25% and the other 35%.

ps In the OP I should have said over the course of any time period instead of one year but that won’t change the problem.

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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15-01-2016, 07:20 AM
RE: Math Problem - help
(15-01-2016 07:10 AM)Full Circle Wrote:  
(15-01-2016 07:01 AM)onlinebiker Wrote:  Now you're off into fantasyland.



Show me ANY investment that can guarantee just a 20 percent guaranteed payback, and I'll kiss your ass.....

Wink

Pucker up baby.

I never said guaranteed. I have two similar investments, over the course of the last seven years one has returned 25% and the other 35%.

ps In the OP I should have said over the course of any time period instead of one year but that won’t change the problem.

In order to be "hard numbers" -- and therefore calculable - it must be guaranteed.

.....

Or, we could just take a guess...........

Smile

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15-01-2016, 07:23 AM (This post was last modified: 15-01-2016 09:56 AM by unfogged.)
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

That tells you how much you'd have at the end if you want to end up with the same total, not the same gain. To match the gain you need to not include the initial investment

.25y=.35x
y=.35x/.25
y=1.4x

There is no single answer unless you have a target gain in mind

$100 at 35% returns $135, $140 at 25% returns $175, both gain $35
$150 at 35% returns $202.50, $210 at 25% returns $262.50, both gain $52.50
etc

With your original 1.08 multiplier to get the same end result instead of the same gain:
$100 at 35% returns $135, $108 at 25% returns $135
$150 at 35% returns $202.50, $162 at 25% returns $202.50
etc

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15-01-2016, 07:54 AM
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 don`t know why are you over complicating this.

Out of my head you need to invest 0.926$ on a 35% return investment for every 1$ on a 25% return investment.
Or for every 1$ you invest on a 35% return , you have to invest 1.08$ on a 25% return investment. However you want to look at it.

Or in a example 1000$ *1.25 = 926$*1.35 = 1250$

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15-01-2016, 08:57 AM
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 will tell you the answer if you tell me what those investments are. Consider

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15-01-2016, 12:39 PM
RE: Math Problem - help
(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.

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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15-01-2016, 12:43 PM
RE: Math Problem - help
(15-01-2016 07:54 AM)Slowminded Wrote:  I don`t know why are you over complicating this.

Out of my head you need to invest 0.926$ on a 35% return investment for every 1$ on a 25% return investment.
Or for every 1$ you invest on a 35% return , you have to invest 1.08$ on a 25% return investment. However you want to look at it.

Or in a example 1000$ *1.25 = 926$*1.35 = 1250$

Thanks. I like to make things difficult for myself Weeping

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).

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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15-01-2016, 12:58 PM
RE: Math Problem - help
(15-01-2016 12:43 PM)Full Circle Wrote:  
(15-01-2016 07:54 AM)Slowminded Wrote:  I don`t know why are you over complicating this.

Out of my head you need to invest 0.926$ on a 35% return investment for every 1$ on a 25% return investment.
Or for every 1$ you invest on a 35% return , you have to invest 1.08$ on a 25% return investment. However you want to look at it.

Or in a example 1000$ *1.25 = 926$*1.35 = 1250$

Thanks. I like to make things difficult for myself Weeping

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 basically need two equations to solve for two variables. You already had one: 1.35x = 1.25y. now you have a second one: x + y = 100. Solving simultaneously, you get x = $48.08, y = $51.92. Multiplying those by the appropriate return rates, both totals will be $64.90. Adjusting this for any particular initial amount, you would want to put 48.08% of the amount in the fund that returns 35%, and 51.92% in the fund that returns 25%.
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