How much money was invested at each rate?

Question

A mother wants to invest $7000 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 $420, how much money was invested at each rate?

Answer 1

Amanda,

Let x = dollar amount invested in CDs at 4% annual interest.

Then 7000 - x = amount invested in Bonds at 7% interest.

Total Interest in year = 0.04*x + 0.07*(7000 - x) = 420

Expanding, 0.04*x + 490 - 0.07*x = 420

And simplifying: -0.03x = 420 - 490 = -70

So x = -70/-0.03 or x = 2,333.33 invested in CDs

And 7000 - x = 4666.67 invested in Bonds