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 $15000. the amount invested at 4% 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 $15000. the amount invested at 4% is $

Answer

Explanation:

Step1: Let the amount invested at 2% be $x$. Then the amount invested at 4% is $18000 - x$.

Let $x$ be the amount at 2%. So amount at 4% is $18000 - x$.

Step2: Set up the interest - equation.

The interest from the 2% account is $0.02x$ and from the 4% account is $0.04(18000 - x)$. The total interest is $420$. So, $0.02x+0.04(18000 - x)=420$.

Step3: Expand and simplify the equation.

$0.02x + 720-0.04x=420$. Combine like - terms: $720-(0.04x - 0.02x)=420$, which gives $720 - 0.02x=420$.

Step4: Solve for $x$.

Subtract 720 from both sides: $-0.02x=420 - 720=-300$. Then divide both sides by $- 0.02$: $x=\frac{-300}{-0.02}=15000$.

Step5: Find the amount invested at 4%.

Since the total amount invested is $18000$ and $x = 15000$ (amount at 2%), the amount invested at 4% is $18000 - 15000 = 3000$.

Answer:

$3000$