Applications of Linear Systems

Question

A financial planner wants to invest $8000, some in stocks earning 15% annually and the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of $930 annually from the two investments.

Answer 1

Since the total investment is $8000, let's assign S for the amount in stocks, and B for the amount in bonds. That gives us:

 

S + B = 8000

 

Now, for a total return of 930 dollars, with 15% earnings for stocks (0.15*S dollars) and 6% earnings for bonds (0.06*B dollars):

 

0.15 S + 0.06 B = 930

 

We could then solve this system of two linear equations by substitution or elimination to get B=3000, S=5000