Kelly has $20,000 to invest and wants to earn $1390 in interest in the first yea

Question

Kelly has $20,000 to invest and wants to earn $1390 in interest in the first year. She wants her investment in treasury bills to be $3000 more than her investment in corporate bonds. The expected returns (in simple interest) on each investment are

Treasury Bills: 5% Treasury Bonds: 7% Corporate Bonds: 10%

How much should she invest in each one?


Pleas give step by step instructions on how to solve this. I need all steps to understand and learn the process to complete the next one on my own....
Thanks :)

Explanation / Answer

There are 3 variables in this equation, so you know that we have to use three equations. First, though, let's name the three variables.
a = amount of money invested in treasury bills
b = amount of money invested in treasury bonds
c = amount of money invested in corporate bonds
Now, let's write out the three equations:

"$20,000 to invest"-->a+b+c=20000
"earn $1390 in interest in the first year"--> .05a+.07b+.1c=1390
      *Because you are just doing the interest after the 1st year, you just use the percentages
"investment in treasury bills to be $3000 more than her investment in corporate bonds"-->a-c=3000

To solve this, you have to use a systems of equation approach. Since the last equation is already simplified to just two variables (a and c), let's figure out a way to get the first two equations so that there is only one with 2 variables (a and c). In other words, let's use the elimination method to "cancel out" the b.

First, multiply the first equation by 7 and the second equation by 100. Now you have:

7a+7b+7c=140000

5a+7b+10c=139000

Now subtract the second from the first and you get: 2a-3c=1000

Now multiply the thrid original equation (a-c=3000) by 2 and subtract from the 2a-3c=1000

2a-3c=1000

2a-2c=6000

-c=-5000, so c=5000

Yay! so the amount invested in the corporate bonds is $5000.

Now figure out a with the original 3rd equation: a-5000=3000, so a=8000

The amount invested in treasury bills is $8000

To find the amount invested in the treasury bonds, you can plug both the a and c values into the first original equation, so 8000+b+5000=20000

so b=7000, so the amount invested in the treasury bonds in $7000

You can check the answers by plugging them back into a different equation

Hope this helps and good luck!

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