Question

betty, a recent retiree, requires $8,000 per year in extra income. she has $50,000 to invest and can invest in b - rated bonds paying 17% per year or in a certificate of deposit (cd) paying 7% per year. how much money should be invested in each to realize exactly $8,000 in interest per year?
the amount of money invested at 17% = $
the amount of money invested at 7% = $

Explanation:

Step1: Define Variables

Let \( x \) be the amount invested at 17% and \( y \) be the amount invested at 7%. We know two things: the total amount invested is $50,000, so LXI2. The total interest is $8,000, and interest is calculated as principal times rate, so \( 0.17x + 0.07y = 8000 \).

Step2: Solve the System of Equations

From the first equation, we can express \( y \) as \( y = 50000 - x \). Substitute this into the second equation:

$$ 0.17x + 0.07(50000 - x) = 8000 $$

Expand the equation:

$$ 0.17x + 3500 - 0.07x = 8000 $$

Combine like terms:

$$ 0.10x + 3500 = 8000 $$

Subtract 3500 from both sides:

$$ 0.10x = 4500 $$

Divide both sides by 0.10:

$$ x = \frac{4500}{0.10} = 45000 $$

Step3: Find \( y \)

Now that we know \( x = 45000 \), substitute back into \( y = 50000 - x \):

$$ y = 50000 - 45000 = 5000 $$

Answer:

The amount of money invested at 17% = $45000
The amount of money invested at 7% = $5000