find the amount invested at each rate.

Question

Mitchell invested part of his $13,000 advance at 5% annual simple interest and the rest at 9% annual simple interest. If his total yearly interest from both accounts was $930, find the amount invested at each rate.

What is the amount invested at 5%?

What is the amount invested at 9%?

Answer 1

Let x be the principle deposited at 5% annual interest and y by the principle deposited at 9% annual interest. Set up and solve the following system of linear equations:

 

1.05x + 1.09y = 13930

x + y = 13000

 

Solve for one in terms of the other and substitute:

 

y = 13000 - x

1.05x + 1.09(13000 - x) = 13930

1.05x + 14170 - 1.09x = 13930

-0.04x = -240

x = 6000

y = 13000 - 6000 = 7000

 

Milton deposited $6000 at 5% and $7000 at 9%.

 

Comment: He should have deposited all $13,000 at 9%.