Q.78 - Precalculus Enhanced with Graphing Utilities

Question

Kelly has \(20,000 to invest. As her financial

planner, you recommend that she diversify into three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple interest, and corporate bonds that yield 10% simple interest. Kelly wishes to earn \)1390 per year in income. Also, Kelly wants her investment in Treasury bills to be $3000

more than her investment in corporate bonds. How much money should Kelly place in each investment?

Step-by-Step Solution

Answer

it is necessary to invest 8000 in treasure bills, 7000 in treasury bonds and 5000 in corporate bonds.

Step 1: Given information

Kelly has $20,000 to invest. As her financial

planner, you recommend that she diversify into three investments.

Step 2: Find the equations

let x be treasure bills , y be treasure bonds, z be corporate bonds

Hence we get the equations

$$\begin{gathered} x+y+z=20000 \left(1\right) \\ 0.05x+0.07y+0.1z=1390 \left(2\right) \\ x-z=3000 \left(3\right) \end{gathered}$$

Substitute equation 3 in equation 1 and 2 we get

$$\begin{gathered} y+2z=17000 \left(4\right) \\ 0.07y+0.15z=1240 \left(5\right) \end{gathered}$$

Multiply equation 4 by 0.07

And subtract from 5

$-0.07x-0.14z=-1190+0.07x+0.15z=12400.01z=50$

We get, $z=5000$

Find the value of y

$$\begin{gathered} y+2z=17000 \\ y+10000=17000 \\ y=7000 \end{gathered}$$

Similarly find the value of x

$$\begin{gathered} x=z+3000 \\ x+5000+3000 \\ x=8000 \end{gathered}$$

Step 3: Conclusion

it is necessary to invest 8000 in treasure bills, 7000 in treasury bonds and 5000 in corporate bonds.