Problema Solution
A loan officer at bank has $1000000 to lend and is required to obtain an average return of 18% per year If she can lend at the rate of 19% or the rate of 16% how much she lend at the 16% rate and still meet her new requirement
Answer provided by our tutors
The loan officer is required to make 18% of $1,000,000 or 0.18*10*6 = $180,000 on any combination of loans.
Let x = amount loaned at 16%.
This will have a return of: 16% of $x = 0.16x dollars.
Then 1,000,000 - x = amount loaned at 19%.
This will return: 0.19(1000000 - x) dollars.
Together, these returns must equal $180,000 thus we have
0.16x + 0.19(1000000 - x) = 180000
by solving we find
x = 1,000,000/3
x = $333,333.333
click here to see the step by step solution of the equation
1,000,000 - x = (2/3)1,000,000 = $666,666.667
the loan officer should loan one-third of the million at 16% and the rest of it (two-thirds) at 19%.