Question 1207743: Banking Wendy,a loan officer at a bank,has $1,000,000 to lend and is required to obtain an average return of 18% per year.If she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Banking Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain
an average return of 18% per year. If she can lend at the rate of 19% or at the rate of 16%,
how much can she lend at the 16% rate and still meet her requirement?
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Let x be the amount, in dollars, loaned out at 16%.
Then the rest, 1000000-x dollars, are loaned out at 19%.
Write an equation for the returned amount
0.16x + 0.19*(1000000-x) = 0.18*1000000
Simplify and find x
0.16x + 190000 - 0.18x = 180000
0.16x - 0.19x = 180000 - 190000
0.03x = 10000
x = 10000/0.03 = 333333.33 (rounded).
ANSWER. She should lend $333,333.33 at 16%.
CHECK. 0.16*333333.33 + 0.19*(1000000-333333.33) = 180000 dollars,
which is 18% return. ! correct !
Solved.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is an informal solution to compare with the formal algebraic solution shown by the other tutor.
Observe that 18% is  of the way from 16% to 19%.
That means that, to average a return of 18%, of the money must be loaned at the higher rate.
So she can lend 1/3 of the money at the lower 16% rate.
ANSWER: 1/3 of $1,000,000, which is $333,333.33
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