Please help

cheesecake

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12 A company offers a $1000 cash loan to anyone earning a monthly salary of at least $2000. To secure the loan, the borrower signs a contract with a promise to repay the $1000 plus a fixed fee before 3 months have elapsed. Failure to do this gives the company a legal right to take $1540 from the borrower’s next salary before returning any amount that has been repaid. From past experience, the company predicts that 70% of borrowers succeed in repaying the loan plus the fixed fee before 3 months have elapsed.
a Calculate the fixed fee that ensures the company an expected 40% profit from each $1000 loan.
b Assuming that the company charges the fee found in part a, how would it be possible, without changing the loan conditions, for the company’s expected profit from each $1000 loan to be greater than 40%?
 

HallsofIvy

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That is an illegal contract since it could result in usury!
 

Jomo

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This forum being a math help forum and not a homework service site I doubt that anyone here will solve your problem for you.
Please read the posting guideline and submit a post following those guidelines.
 

cheesecake

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This forum being a math help forum and not a homework service site I doubt that anyone here will solve your problem for you.
Please read the posting guideline and submit a post following those guidelines.
I am really confuse as what to do here. Do i find the parameter first? using 70% and...
I am not expecting free answer. just some hint to go on...
 

HallsofIvy

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12 A company offers a $1000 cash loan to anyone earning a monthly salary of at least $2000. To secure the loan, the borrower signs a contract with a promise to repay the $1000 plus a fixed fee before 3 months have elapsed. Failure to do this gives the company a legal right to take $1540 from the borrower’s next salary before returning any amount that has been repaid. From past experience, the company predicts that 70% of borrowers succeed in repaying the loan plus the fixed fee before 3 months have elapsed.
a Calculate the fixed fee that ensures the company an expected 40% profit from each $1000 loan.
40% of $1000 is 0.4(1000)= $400.

b Assuming that the company charges the fee found in part a, how would it be possible, without changing the loan conditions, for the company’s expected profit from each $1000 loan to be greater than 40%?
If some of the people were unable to pay back the loan in three months. Then the company would make $1540 which is 154% of $1000.

Another example of the MAN putting down the people! Workers of the world, arise!
 

cheesecake

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t
40% of $1000 is 0.4(1000)= $400.


If some of the people were unable to pay back the loan in three months. Then the company would make $1540 which is 154% of $1000.

Another example of the MAN putting down the people! Workers of the world, arise!
Thank you for your help, but i dont think those are the answer as this is probability distribution question. Thank you once again
 

Dr.Peterson

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12 A company offers a $1000 cash loan to anyone earning a monthly salary of at least $2000. To secure the loan, the borrower signs a contract with a promise to repay the $1000 plus a fixed fee before 3 months have elapsed. Failure to do this gives the company a legal right to take $1540 from the borrower’s next salary before returning any amount that has been repaid. From past experience, the company predicts that 70% of borrowers succeed in repaying the loan plus the fixed fee before 3 months have elapsed.
a Calculate the fixed fee that ensures the company an expected 40% profit from each $1000 loan.
b Assuming that the company charges the fee found in part a, how would it be possible, without changing the loan conditions, for the company’s expected profit from each $1000 loan to be greater than 40%?
The wording of (a) makes you think they want to be sure of a 40% profit from each and every loan, but this seems to be about expected value.

There are two events: the borrower repays the loan in time, or he doesn't. What is the probability of each event?

What is the gain to the company of each event?

How do you calculate expected value?

Please show some work, so we can see where you need help. It may be anywhere from interpreting the bizarre problem, to knowing what expected value is.
 

cheesecake

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The wording of (a) makes you think they want to be sure of a 40% profit from each and every loan, but this seems to be about expected value.

There are two events: the borrower repays the loan in time, or he doesn't. What is the probability of each event?

What is the gain to the company of each event?

How do you calculate expected value?

Please show some work, so we can see where you need help. It may be anywhere from interpreting the bizarre problem, to knowing what expected value is.
This is what my workng is
a.let x be the fee
0.7(1000+x) +0.3(1540)=1400
x=340
 

Dr.Peterson

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This is what my workng is
a.let x be the fee
0.7(1000+x) +0.3(1540)=1400
x=340
That's what I got, assuming I am interpreting the question correctly.

I don't know what they expect you to say for (b).
 

cheesecake

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That's what I got, assuming I am interpreting the question correctly.

I don't know what they expect you to say for (b).
Thank you for your hint.
for b. i guess it should be less than 70% able to pay the loan since the company profits more from those unable to pay within 3 months
 
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