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bantuair






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No One has ever Solved This One
posted on: 2/1/2005 9:06:33 AM

I am yet to find anyone with a solution to this one so consider this a challenge:

I would like to borrow some money from 2 gentlemen. The first one is willing to lend me on a 1 for 1 basis (i.e. for every pound I borrow I have to pay him back the principle plus an additional pound for his troubles). The second is willing to lend me on a 1 to 2 basis, (i.e. for every pound I borrow I have to pay him back the original pound plus 2 pound for his troubles). (Disregard time here)

Now if I know one of them is definately going to die tommorow after lending me the money (don't know which one of them). If one of them dies then the debt is written off and I keep the money. What is the formula for calculating how much I have to borrow from each one to ensure that I make a profit from my keepings should either one of the die?

Thanks
cramwit




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This message was updated on 5/10/2007 5:22:48 PM by cramwit

No One has ever Solved This One
replied on: 5/10/2007 5:16:47 PM

gentleman 'a' lends 1 expecting repayment of 2
gentleman 'b' lends 1 expecting repayment of 3

a ( 1 +(-2)) & b ( 1 +(-3))
with the negative terms for whichever dies zeroed out
so,
possible a dies & b doesn't
a ( 1 + (0)) + b ( 1 +(-3))
= a + b ( -2 )
= a - 2b

other case b dies & a doesn't

a ( 1 +(-2)) + b ( 1 +(0))
= a ( -1 ) + b
= b - a

so both a - 2b > 0 & b - a > 0 to profit
a > 2b & b > a
b > a > 2b
since b > 2b ; b must be negative
& a must be between b & 2b

so there is no obvious answer.

If you have initial capital/money then you can use the above calculations to proportion the transactions of lending proportions to each to insure you get your money returned. And to maximize a guaranteed profit, a should be precisely 1.5 b & b should be as big as conditions allow.

If both are going to die you should borrow
as much from both as possible

The only way you can borrow a negative amount is if you are a lender.

now if neither were going to die & b was an excellent credit risk & you have no money to start with, then you borrow as much from a as b wants to borrow from you at his going rate. ie. you profit from the interest differential.

The question, taken as given has no 'good' answer as far as i can see.
cramwit




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This message was updated on 5/10/2007 5:24:53 PM by cramwit

No One has ever Solved This One
replied on: 5/10/2007 5:17:29 PM

The kamikaze solution.

You borrow as much as possible from both,
give it to your wife &/or kids & then you die.
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