Chapter 11.1, Problem 78AYU

To determine

To calculate: The amount of money that Kelly should place in each investment.

Answer to Problem 78AYU

The amount placed in treasury bill is $\$8000$ , in treasury bond is $\$7000$ and corporate bond is $\$5000$ .

Explanation of Solution

Given information:

The amount of money that Kelly has to invest is $\$20,000$ . She divided this into three investment, first are the treasury bills that yield $5\%$ simple interest, treasury bond that yield $7\%$ simple interest and corporate bond that yield $10\%$ simple interest. Kelly wants to earn $\$1390$ per year in income. As per her requirement investment in treasury bills must be $\$3000$ more than her investment in corporate bonds.

Calculation:

Consider the provided information that the amount of money that Kelly has to invest is $\$20,000$ . She divided this into three investment, first are the treasury bills that yield $5\%$ simple interest, treasury bond that yield $7\%$ simple interest and corporate bond that yield $10\%$ simple interest. Kelly wants to earn $\$1390$ per year in income. As per her requirement investment in treasury bills must be $\$3000$ more than her investment in corporate bonds.

Let the amount of money placed in treasury bill is x, in treasury bonds is y and corporate bonds are z.

The amount of money that Kelly has to invest is $\$20,000$ .

So, the equation is $x+y+z=20000$

She divided this into three investment, first are the treasury bills that yield $5\%$ simple interest, treasury bond that yield $7\%$ simple interest and corporate bond that yield $10\%$ simple interest. Kelly wants to earn $\$1390$ per year in income.

So, the equation is $0.05x+0.07y+0.1z=1390$

As per her requirement investment in treasury bills must be $\$3000$ more than her investment in corporate bonds.

So, the equation is $x-z=3000$

So, the system of equation so formed is,

  $\begin{array}{c}x+y+z=20000\\ 0.05x+0.07y+0.1z=1390\\ x-z=3000\end{array}$

Add $x+y+z=20000$ and $x-z=3000$ to obtain $2x+y=23000$

Multiply $x-z=3000$ by 0.1 and add with $0.05x+0.07y+0.1z=1390$ to obtain

  $0.15x+0.07y=1690$

Multiply $2x+y=23000$ by 0.07 and subtract from $0.15x+0.07y=1690$ .

Therefore, $x=8000$ and $y=7000$ .

Now substitute $x=8000$ in equation $x-z=3000$ .

Therefore, $z=5000$

Thus, the amount placed in treasury bill is $\$8000$ , in treasury bond is $\$7000$ and corporate bond is $\$5000$ .