you invested $18,000 in two accounts paying 2% and 4% annual interest, respectively. if the total interest…

you invested $18,000 in two accounts paying 2% and 4% annual interest, respectively. if the total interest earned for the year was $420, how much was invested at each rate? the amount invested at 2% is $□.

you invested $18,000 in two accounts paying 2% and 4% annual interest, respectively. if the total interest earned for the year was $420, how much was invested at each rate? the amount invested at 2% is $□.

Answer

Explanation:

Step1: Let the amount invested at 2% be $x$.

Then the amount invested at 4% is $(18000 - x)$.

Step2: Calculate the interest from each account.

The interest from the 2% - account is $0.02x$, and the interest from the 4% - account is $0.04(18000 - x)$.

Step3: Set up the interest - total equation.

The total interest is $420$, so $0.02x+0.04(18000 - x)=420$.

Step4: Expand and simplify the equation.

$0.02x + 720-0.04x=420$. Combining like terms gives $- 0.02x=420 - 720=-300$.

Step5: Solve for $x$.

Dividing both sides by $-0.02$, we get $x=\frac{-300}{-0.02}=15000$.

Answer:

$15000$