Question

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%?

Answer 1

Answer:

${ {3}^{2} }^{3}  \times  {(2 \times  {3}^{5}) }^{ - 2}  \times  {18}^{2 }  \\  \\  =  {3}^{6}  \times  \frac{1}{4 \times  {3}^{10} }  \times  {18}^{2}  \\  \\  =  \frac{ {18}^{2} }{4 \times  {3}^{4} }  \\  \\  =  \frac{ \cancel{18 } \: ^{ \cancel{6}} \: ^{ \cancel{2}}\times { \cancel{18}}  \: ^{ \cancel{6 }} \:  ^{ \cancel{2}} \:  ^1 }{ { \cancel{4 }\:_1}\times { \cancel{3} \: _1} \times { \cancel{3 } \: _1}\times { \cancel{3} \:_1} \times { \cancel{3} \: _1} }  \\  \\  = { \huge{ \red{ \boxed{1}}}}$