Steve has $25,000 to invest and wishes to earn an overall annual rate of return of 8%. His financial advisor recommends that he invest some of the money in a 5-year CD paying 5% per annum and the rest in a corporate bond paying 9% per annum. How much should be placed in each investment in order for Steve to achieve his goal?

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

[tex]x+y=25,000[/tex]

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

[tex]0.05x+0.09y=0.08(x+y)[/tex]

Rearranging:

[tex]0.05x+0.09y=0.08x+0.08y[/tex]

Simplifying

[tex]0.01y=0.03x[/tex]

Multiplying by 100

[tex]y=3x[/tex]

Substituting in the first equation

[tex]x+3x=25,000\\4x=25,000\\x=6,250[/tex]

And therefore

[tex]y=25,000-6,250=18,750[/tex]

Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond