Question

A mother wants to invest $6000 for her children's education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $360, how much money was invested at each rate?

Answer 1

Let X equal the amount of money invested in the CD.

As the question states that the remainder of the $6,000 will be invested in the savings bond, you can define the amount invested in the savings bond as 6,000 – X.
Once you have the terms defined in this way, you can then create an easy equation to solve for X.

The interest after 1 year ($360) will be equal to the amount of money in the CD (X) multiplied by the interest rate on the CD (4%) plus the amount of money in the savings bond (6,000 – X) multiplied by the interest rate on the savings bond (7%).

The equation will look like this:

(X)(0.04) + (6,000 - X)(0.07) = 360

From here, collect like terms on the left side and then isolate X.

0.04X + 420 – 0.07X = 360
-0.03X = -60
X = -60 / -0.03
X = 2,000

Therefore, the amount invested in the CD was $2,000 and the amount invested in the savings bond was the remaining $4,000. To double check if this is correct, you can multiply these amounts by the corresponding interest rate and it should add up to the total interest earned.

2,000 x 0.04 = 80
4,000 x 0.07 = 280

280 + 80 = 360

Hope this helps!