Betsy a recent retiree requires 5000 per year in extra income she has 70000 to invest and can invest in B rated bonds paying 15 percent per year or in a certificate of deposit paying 7 percent per year how much money should be invested in each to realize exactly 5000 in interest per year

We need to find out how much Betsy should invest in each type of account to generate exactly $5,000 in interest per year.

Let:
- $ x $ = amount invested in B-rated bonds (which pay 15% interest per year),
- $ y $ = amount invested in the certificate of deposit (which pays 7% interest per year).

We have two pieces of information:
1. Betsy has $70,000 to invest in total. Therefore:
   \[
   x + y = 70,000
   \]
2. Betsy needs exactly $5,000 in interest per year. The interest from the B-rated bonds and the certificate of deposit should add up to $5,000. Therefore:
   \[
   0.15x + 0.07y = 5,000
   \]

Now, we have a system of two equations:

\[
1. \quad x + y = 70,000
\]
\[
2. \quad 0.15x + 0.07y = 5,000
\]

### Step 1: Solve for one variable
From the first equation, solve for $ y $ in terms of $ x $:
\[
y = 70,000 - x
\]

### Step 2: Substitute this into the second equation
Substitute $ y = 70,000 - x $ into the second equation:
\[
0.15x + 0.07(70,000 - x) = 5,000
\]

### Step 3: Simplify and solve for $ x $
\[
0.15x + 0.07(70,000 - x) = 5,000
\]
\[
0.15x + 0.07 \times 70,000 - 0.07x = 5,000
\]
\[
0.15x + 4,900 - 0.07x = 5,000
\]
\[
0.08x + 4,900 = 5,000
\]
\[
0.08x = 5,000 - 4,900
\]
\[
0.08x = 100
\]
\[
x = \frac{100}{0.08} = 1,250
\]

### Step 4: Solve for $ y $
Substitute $ x = 1,250 $ into the first equation:
\[
1,250 + y = 70,000
\]
\[
y = 70,000 - 1,250 = 68,750
\]

### Final Answer:
Betsy should invest:
- $1,250 in B-rated bonds,
- $68,750 in the certificate of deposit.

This will yield exactly $5,000 in interest per year.

---

Do you want more details, or have any questions?  
Here are 5 related questions for practice:
1. What would happen if the interest on the certificate of deposit was reduced to 6%?
2. How would the investment strategy change if Betsy needed $6,000 in annual interest?
3. What would Betsy’s total interest be if she invested all $70,000 in the B-rated bonds?
4. If Betsy could invest in a third option that pays 10% interest, how would that impact her allocation?
5. How long would it take for Betsy’s investment to double if she reinvested the interest at 7% annually?

**Tip:** When solving systems of equations, substitution is a handy method when one variable is easy to express in terms of the other.

Betsy, a recent retiree, requires $5,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit paying 7% per year. How much money should be invested in each to realize exactly $5,000 in interest per year?

Learn how to solve a real-world financial problem: Betsy needs to invest $70,000 to earn $5,000 in interest per year by choosing between B-rated bonds at 15% interest and certificates of deposit at 7%. This algebraic solution uses a system of linear equations and the substitution method. Suitable for high school students and financial enthusiasts.

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