Betsy, a recent retiree, requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 17% per year or in a CD paying 7% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
I do not know what to do for this.
ok, so Betsy invest part of her $70,000 in B-rate bonds paying 17% per year
.17x
the rest of the $70,000 she invest in a CD paying 7% per year
.07(70000-x)
totally she wants to get $6,000 per year
= 6000
putting this all together:
.17x + .07(70000-x) = 6000
solve for x. that will give how much she invested in B-rated bonds. plug that in 70000-x to find how much she invested in a CD
$11,000
To determine how much money should be invested in each option, we need to set up an equation based on the given information.
Let's assume x represents the amount invested in B-rated bonds and y represents the amount invested in the CD.
Based on the information provided, we know that the total amount invested is $70,000, so we have:
x + y = 70,000 ...(Equation 1)
We also know that the interest earned from the B-rated bonds is 17% of x, while the CD earns 7% of y. The sum of the interest earned from both investments should equal $6,000, so we have:
0.17x + 0.07y = 6,000 ...(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.
To solve the system of equations, we can use substitution or elimination. Here, we will use the substitution method.
From Equation 1, we can rewrite it in terms of x as:
x = 70,000 - y
Substitute this value of x in Equation 2:
0.17(70,000 - y) + 0.07y = 6,000
Simplify and solve for y:
11,900 - 0.17y + 0.07y = 6,000
11,900 - 0.10y = 6,000
-0.10y = 6,000 - 11,900
-0.10y = -5,900
y = -5,900 / (-0.10)
y = 59,000
Now, we know that y (amount invested in the CD) is $59,000. To find x (amount invested in B-rated bonds), substitute this value into Equation 1:
x + 59,000 = 70,000
x = 70,000 - 59,000
x = 11,000
Therefore, Betsy should invest $11,000 in B-rated bonds and $59,000 in the CD to realize exactly $6,000 in interest per year.
To determine how much money Betsy should invest in each option to earn $6,000 in interest per year, we can set up a system of equations.
Let's assume Betsy invests x dollars in B-rated bonds and y dollars in a CD. The interest she earns from each investment can be calculated as follows:
Interest from B-rated bonds: 0.17x
Interest from CD: 0.07y
According to the given information, Betsy requires $6,000 per year in extra income. Therefore, we can write the first equation:
0.17x + 0.07y = 6,000
Additionally, we know that Betsy has $70,000 to invest, so the second equation is:
x + y = 70,000
We now have a system of two equations:
0.17x + 0.07y = 6,000
x + y = 70,000
To solve this system, we can use substitution or elimination.
Let's solve it using the elimination method:
Multiply the second equation by 0.17 to make the coefficients of x equal:
0.17(x + y) = 0.17(70,000)
0.17x + 0.17y = 11,900
Now we can subtract the second equation from the modified equation:
(0.17x + 0.07y) - (0.17x + 0.17y) = 6,000 - 11,900
0.17y - 0.17y + 0.07y - 0.17y = -5,900
Combine like terms:
-0.10y = -5,900
Divide both sides of the equation by -0.10 to solve for y:
y = -5,900 / -0.10
y = 59,000
Now that we have the value of y, we can substitute it back into the second equation to solve for x:
x + 59,000 = 70,000
x = 70,000 - 59,000
x = 11,000
Therefore, Betsy should invest $11,000 in B-rated bonds and $59,000 in a CD to realize exactly $6,000 in interest per year.