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?

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

Step-by-step explanation:

System of Equations

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

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

Rearranging:

Simplifying

Multiplying by 100

Substituting in the first equation

And therefore

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