Ernest receives $555 per year from his $7000 investment in municipal and corporate bonds. His municipal bonds pay 6% and his corporate bonds pay 9%. How much money is invested in each type of bond
Solve these two equations for M and C, the amounts invested in munis and corporates, respectivly.
M + C = 7000
0.06M + 0.09 C = 555
Using substitution,
0.06M + 0.09*(7000 - M) = 555.
Rearranging the last equation,
0.03 M = 630 - 555 = 75
M = 75/0.03 = _____
C = 7000 - M = ____
Let's assume Ernest invests x dollars in municipal bonds and y dollars in corporate bonds.
From the given information, we know that the sum of the amounts Ernest receives from his investments is $555 per year.
The interest Ernest receives from his municipal bonds is calculated by multiplying the amount invested in municipal bonds (x) by the interest rate of 6% (or 0.06). Therefore, the interest from municipal bonds is 0.06x.
The interest Ernest receives from his corporate bonds is calculated by multiplying the amount invested in corporate bonds (y) by the interest rate of 9% (or 0.09). Therefore, the interest from corporate bonds is 0.09y.
According to the question, the sum of these two interest amounts is $555:
0.06x + 0.09y = 555 ---(Equation 1)
The total amount Ernest invested is $7000, so x + y = 7000. ---(Equation 2)
Now we have a system of equations consisting of Equation 1 and Equation 2. We can solve this system to find the values of x and y.
To determine the amount of money invested in each type of bond, we need to set up a system of equations.
Let's assume Ernest invested x dollars in municipal bonds and y dollars in corporate bonds.
Based on the given information, we can write two equations:
1. The sum of the investments:
x + y = $7000
2. The annual income from the investments:
0.06x + 0.09y = $555
Now we can solve the system of equations to find the values of x and y.
One way to solve this system is by substitution. We can solve the first equation for x in terms of y:
x = $7000 - y
Substituting this into the second equation, we get:
0.06($7000 - y) + 0.09y = $555
Distributing and simplifying:
$420 - 0.06y + 0.09y = $555
Combining like terms:
0.03y = $135
Dividing both sides by 0.03:
y = $4500
Now, substitute the value of y back into the first equation to find x:
x + $4500 = $7000
x = $7000 - $4500
x = $2500
Therefore, Ernest has invested $2500 in municipal bonds and $4500 in corporate bonds.
M=2,500
C=4,500