Final answer:
The executive invested $19,000 at a 7% interest rate and $20,000 at a 6% interest rate to achieve the annual return of $2,530. This was solved using a system of linear equations to relate the amounts invested at each interest rate to the total return.
Step-by-step explanation:
The student is asking how to divide an investment of $39,000 between two different interest rates to achieve a specified return. To solve this, we'll use a system of equations. Let's call the amount invested at 7% x and the amount invested at 6% y. The first equation represents the total investment:
x + y = $39,000
The second equation represents the total annual return:
0.07x + 0.06y = $2,530
Now we solve the system of equations. We can start by expressing y in terms of x from the first equation:
y = $39,000 - x
Then we substitute this expression for y in the second equation:
0.07x + 0.06($39,000 - x) = $2,530
Expanding and simplifying this equation, we get:
0.07x + $2,340 - 0.06x = $2,530
0.01x = $190
Divide both sides by 0.01 we find x = $19,000. Substituting x back into y = $39,000 - x, we get:
y = $39,000 - $19,000
y = $20,000
Therefore, the executive invested $19,000 at 7% and $20,000 at 6%.