Answer:
<em>Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond</em>
Step-by-step explanation:
<u>System of Equations</u>
We need to find how Steve will distribute his investments between two possible options: one of them will pay 5% per annum and the other will pay 9% per annum. We know Steve has $25,000 to invest and wants to have an overall annual rate of return of 8%.
Let's call x to the amount Steve will invest in the CD paying 5% per annum and y to the amount he will invest in a corporate bond paying 9% per annum.
The total investment is $25,000 which leads to the first equation
![x+y=25,000](https://tex.z-dn.net/?f=x%2By%3D25%2C000)
If x dollars are invested at 5%, then the interest return is 0.05x. Similarly, y dollars at 9% return 0.09y. The overall return is 8% on the total investment, thus
![0.05x+0.09y=0.08(x+y)](https://tex.z-dn.net/?f=0.05x%2B0.09y%3D0.08%28x%2By%29)
Rearranging:
![0.05x+0.09y=0.08x+0.08y](https://tex.z-dn.net/?f=0.05x%2B0.09y%3D0.08x%2B0.08y)
Simplifying
![0.01y=0.03x](https://tex.z-dn.net/?f=0.01y%3D0.03x)
Multiplying by 100
![y=3x](https://tex.z-dn.net/?f=y%3D3x)
Substituting in the first equation
![x+3x=25,000\\4x=25,000\\x=6,250](https://tex.z-dn.net/?f=x%2B3x%3D25%2C000%5C%5C4x%3D25%2C000%5C%5Cx%3D6%2C250)
And therefore
![y=25,000-6,250=18,750](https://tex.z-dn.net/?f=y%3D25%2C000-6%2C250%3D18%2C750)
Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond