Question

Suppose you invested $10,000, part at 6% annual interest and the rest at 9% annual interest. If you received $684 in interest after one year, how much did you invest at each rate?

Answer 1

Answer:

Step-by-step explanation:

Let A be the amount invested at 6% and B be the amount invested at 9%.

 

For example, for A invested for one year we get:

 T = A * ( 1 + 6/100) = A + interest or an interest amount of A * ( .06 ).

Then we know that at one year the total interest is:

 A * ( .06 ) + B * ( .09 ) = 684

and we also know that

 

A + B = 10,000

Solving for A by substituting for B:

 B = 10,000 - A

 A * ( .06 ) + (10,000 - A) * ( .09 ) = 684

 A * ( -.03 ) = 684 - 900 = -216

so  

A = 216 / 0.03 = 7,200

B = 2,800.