Wendy is a loan officer and has 1,000,000 to lend and is required to get 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 16% rate and still meet the requirement?

let the amount loaned out at 16% be $x

so

.16x + .19(1000000 - x) = .18(1000000)

(nice rate of return, must be a question from an "old" textbook)

I DON'T UNDERSTAND WHAT THE ANSWER WOULD BE....

To determine the amount Wendy can lend at a 16% interest rate, we need to understand the concept of weighted average return.

Weighted average return considers the returns from different interest rates and the corresponding proportions of the total amount to calculate the average return.

Let's say Wendy lends an amount, x, at a 19% interest rate. Since she has a total of $1,000,000 to lend, the amount she lends at a 16% interest rate is (1,000,000 - x).

To find the weighted average return, we can use the formula:

Average Return = (Amount Lent at Rate 1 * Interest Rate 1) + (Amount Lent at Rate 2 * Interest Rate 2) / Total Amount Lent

We already know the average return needed is 18%, so we can plug the values into the formula:

18% = (x * 19%) + ((1,000,000 - x) * 16%) / 1,000,000

Simplifying the equation:

0.18 = (0.19x + 0.16(1,000,000 - x)) / 1,000,000

Now we can solve for x:

0.18 * 1,000,000 = 0.19x + 0.16(1,000,000 - x)

180,000 = 0.19x + 160,000 - 0.16x

180,000 - 160,000 = 0.19x - 0.16x

20,000 = 0.03x

Dividing both sides of the equation by 0.03:

x = 20,000 / 0.03

x = $666,667

Therefore, Wendy can lend $666,667 at a 16% interest rate and still meet the requirement of an average return of 18% per year.