A mother wants to invest $15000 for her children's education. She invest a portion of the money in a bank certificate of deposit which earns 4 percent and the remainder in a savings bond which earns 7 percent. If the total interest earned after a year is $900 how much money was invested at each rate?
To solve this problem, let's assume the amount invested in the bank certificate of deposit is x dollars. So, the amount invested in the savings bond will be (15000 - x) dollars.
Now, let's calculate the interest earned from each investment. The interest earned from the bank certificate of deposit is calculated as 4% of x dollars, which is (4/100) * x = 0.04x dollars.
Similarly, the interest earned from the savings bond is calculated as 7% of (15000 - x) dollars, which is (7/100) * (15000 - x) = 0.07(15000 - x) dollars.
According to the problem, the total interest earned from both investments is $900. So, we can write the equation:
0.04x + 0.07(15000 - x) = 900
Now we can solve this equation to find the value of x.
0.04x + 0.07(15000 - x) = 900
0.04x + 1050 - 0.07x = 900
-0.03x = -150
x = -150 / (-0.03)
x = 5000
Therefore, the mother invested $5000 in the bank certificate of deposit and the remaining amount, $10000, in the savings bond.
Let's call the amount of money invested in the bank certificate of deposit (CD) as 'x', and the amount invested in the savings bond as '15000 - x' (since the total investment is $15000).
Given that the CD earns 4% interest, the interest earned for that portion is 0.04x.
Similarly, the savings bond earns 7% interest, so the interest earned for that portion is 0.07(15000 - x).
According to the problem, the total interest earned after a year is $900:
0.04x + 0.07(15000 - x) = 900.
Now, let's solve this equation to find the values of 'x' and '15000 - x':
0.04x + 0.07(15000 - x) = 900
0.04x + 1050 - 0.07x = 900
-0.03x = -150
x = -150 / -0.03
x = 5000.
Therefore, $5000 is invested in the bank certificate of deposit, and the remaining amount ($15000 - $5000 = $10000) is invested in the savings bond.
b + s = 15000
.04 b + .07 s = 900
solve the system for b and s