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Don James wants to invest $66,000 to earn $1381 per year. He can invest in B- rated bonds paying 3.1% per year or in a Certificate of Deposit (CD) paying 1.2% per year. How much money should be invested in each to realize exactly $1381 in interest per year?

User Hao Kung
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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:

User Sudeep
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