To solve this problem, we need to set up a system of linear equations. Let's define the variables first:

• Let $x$ be the amount invested in the B-rated bonds.
• Let $y$ be the amount invested in the certificate of deposit (CD).

Given:

• The B-rated bonds pay 15% interest per year.
• The CD pays 5% interest per year.
• Betsy needs a total of $5,000 in interest per year.
• She has $50,000 to invest in total.

Step 1: Set up the equations

1. Interest Equation: The total interest earned from both investments must equal $5,000: $0.15x + 0.05y = 5000$

2. Total Investment Equation: The total amount invested should equal $50,000: $x + y = 50000$

Step 2: Solve the system of equations

1. Solve the second equation for $y$: $y = 50000 - x$

2. Substitute $y$ in the interest equation: $0.15x + 0.05(50000 - x) = 5000$

3. Simplify and solve for $x$: $0.15x + 2500 - 0.05x = 5000$ $0.10x + 2500 = 5000$ $0.10x = 2500$ $x = 25000$

So, Betsy should invest $25,000 in the B-rated bonds.

4. Find $y$ using $x = 25000$: $y = 50000 - 25000 = 25000$

Conclusion:

Betsy should invest $25,000 in B-rated bonds and $25,000 in the certificate of deposit (CD) to achieve exactly $5,000 in interest per year.

Would you like more details, or do you have any questions?

Here are five related questions:

1. What would happen if Betsy needed $6,000 per year instead of $5,000?
2. How would the investment amounts change if the interest rate on the CD was 6% instead of 5%?
3. What is the total interest earned over 5 years with the current investment plan?
4. What is the effect of risk if Betsy decides to invest more in the B-rated bonds?
5. How does compound interest affect the total interest if the CD compounds annually?

Tip: When dealing with investments, always consider the risk associated with higher interest rates, as they often come with higher risk.