Sue, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
Sue, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
To determine how much money Sue should invest in each option, we need to set up a system of equations based on the given information.
Let's assume Sue invests x dollars in B-rated bonds and y dollars in a certificate of deposit (CD).
According to the given information, the interest earned from the B-rated bonds would be 15% of x dollars, expressed as 0.15x. Similarly, the interest earned from the CD would be 7% of y dollars, expressed as 0.07y.
We also know that Sue requires an extra income of $6,000 per year. Therefore, the sum of the interest earned from the B-rated bonds and the CD should equal $6,000.
Now, we can write the first equation:
0.15x + 0.07y = 6,000
Furthermore, we know that Sue has a total of $50,000 to invest, so the sum of the investments in the B-rated bonds and the CD should equal $50,000.
Hence, we can write the second equation:
x + y = 50,000
Now, we have a system of equations that we can solve to find the values of x and y.
To solve this system of equations, we can utilize various methods, such as substitution or elimination.
Let's use the elimination method to solve this system:
From the second equation, we can express x as 50,000 - y and substitute it into the first equation:
0.15(50,000 - y) + 0.07y = 6,000
Now, we can simplify and solve for y:
7,500 - 0.15y + 0.07y = 6,000
7,500 - 0.08y = 6,000
-0.08y = 6,000 - 7,500
-0.08y = -1,500
y = -1,500 / -0.08
y = 18,750
Now that we have the value of y, which represents the amount invested in the CD, we can substitute it back into the second equation to find x:
x + 18,750 = 50,000
x = 50,000 - 18,750
x = 31,250
Therefore, Sue should invest $31,250 in B-rated bonds and $18,750 in a CD to realize exactly $6,000 in interest per year.
Never mind the algebra. Where can I get that 7% CD?
Seriously, solve this equation:
0.15x + 0.07(50,000-x) = 6000
x is the amount invested in 15% bonds.
50,000 -x is invested in the CD.
The equation can easily be solved in two steps.