Chapter A.8, Problem 20AYU

To determine

To find: How much can she lend at the $16\%$ rate and still meet her requirement?

Answer to Problem 20AYU

$\$333,333.33$ at $16\%$ rate.

Explanation of Solution

Given:

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 $16\%$.

Calculation:

Let $x$ represent how much can she lend at the $16\%$ rate and $M$ represent the $\$1,000,000$.

$0.16x+0.19\left(M-x\right)=0.18M$

$-0.03x=-0.01M$

$x=\frac{0.01M}{0.03}=\$333,333.33$ at $16\%$ rate.