an executive invests $22,000 some at 7% and some at 6% annual interest. If he received an annual return of $1,420, how much is invested at each rate?

Question

 solve

Answer 1

We can assume the X is the amount he invested at 6%,Y is the amount he invested at 7%.

So, based on the question,we can get two equations

X+Y=22000

X*6%+Y*7%=1420

we can change first equation into X=22000-Y and put this one into the second equation.

(22000-Y)*6%+Y*7%=1420

we can solve Y

1320-6%*Y+7%*Y=1420

Y*1%=100

Y=10000

X=22000-Y=22000-10000=12000

The answer is he invested 10000 at 7%, 12000 at 6%.

Answer 2

If we assume that we invest an amount X that returns 7% and an amount Y that returns 6%, we can solve the problem.

 

We first know that X + Y = 22,000 which is the total amount invested

 

Next we know that 0.07X + 0.06Y = 1420

 

Now we have two equations and two unknowns.

 

Solving the first equation for Y yields: Y = 22,000 - X

 

Substitute the value for Y into the second equation:

 

0.07X + 0.06 (22,000 - X) = 1420

0.01X = 1420 - 22,000*.06 = 100

X=100/.01 = $10,000

 

Y = 22,000 - $10,000 = $12,000