Answer:
To determine how much money should be invested in each option to realize exactly $1381 in interest per year, we can set up a system of equations:
Let's represent the amount of money invested in B-rated bonds as "x" and the amount invested in the Certificate of Deposit (CD) as "y."
1. The interest earned from the B-rated bonds can be calculated as 3.1% of the amount invested, which is 0.031x.
2. The interest earned from the CD can be calculated as 1.2% of the amount invested, which is 0.012y.
Since the total interest earned per year should be $1381, we can set up the equation:
0.031x + 0.012y = 1381
Additionally, the total amount invested should be $66,000, so we can set up another equation:
x + y = 66000
We now have a system of equations:
0.031x + 0.012y = 1381
x + y = 66000
To solve this system, we can use substitution or elimination. Let's use elimination:
Multiply both sides of the second equation by 0.012 to make the coefficients of "y" equal:
0.012x + 0.012y = 792
Now, we can subtract the second equation from the first to eliminate "y":
0.031x + 0.012y - (0.012x + 0.012y) = 1381 - 792
0.019x = 589
Divide both sides by 0.019:
x = 589 / 0.019
x ≈ 30947.37
Substitute this value back into the second equation to find "y":
30947.37 + y = 66000
y ≈ 35052.63
Therefore, Don James should invest approximately $30,947.37 in B-rated bonds and $35,052.63 in the Certificate of Deposit (CD) to realize exactly $1381 in interest per year.
Explanation: