A mother wants to invest $5000 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% simple interest and the remainder in a savings bond that earns 5% simple interest. If the total interest earned after one year is $235, how much money was invested in each account?
If there is $x at 4%, the rest (5000-x) is at 5%
So now, just add up the interest
.04x + .05(5000-x) = 235
...
To solve this problem, we can set up a system of equations based on the given information.
Let's say the amount invested in the CD account is x dollars, and the amount invested in the savings bond is y dollars.
The interest earned from the CD account would be 4% of x, which is 0.04x dollars.
The interest earned from the savings bond would be 5% of y, which is 0.05y dollars.
According to the problem, the total interest earned after one year is $235.
So we can write the first equation as:
0.04x + 0.05y = $235 ---- (1)
The total amount invested is $5000, so the second equation can be written as:
x + y = $5000 ---- (2)
Now we have a system of linear equations which we can solve to find the values of x and y.
We can start by multiplying equation (2) by 0.04 to make the coefficients of x in both equations the same:
0.04x + 0.04y = $200 ---- (3)
Now we can subtract equation (3) from equation (1) to eliminate the variable x:
0.04x + 0.05y - (0.04x + 0.04y) = $235 - $200
0.01y = $35
Dividing both sides of the equation by 0.01, we get:
y = $3500
Now we can substitute the value of y into equation (2) to find x:
x + $3500 = $5000
x = $5000 - $3500
x = $1500
Therefore, the mother invested $1500 in the CD account and $3500 in the savings bond.
To summarize:
Amount invested in the CD account: $1500
Amount invested in the savings bond: $3500