You invested 20,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interested earned for the year was $830, how much was invested at each rate?
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To solve this problem, we can set up a system of equations. Let's assume you invested x amount of dollars at 4% interest, and 20,000 - x amount of dollars at 7% interest.
The interest earned from the account with a 4% interest rate can be calculated as x * 0.04, and the interest earned from the account with a 7% interest rate can be calculated as (20,000 - x) * 0.07.
According to the problem, the total interest earned was $830. Therefore, we can write the equation:
x * 0.04 + (20,000 - x) * 0.07 = 830
Now, let's solve this equation step-by-step:
0.04x + 0.07(20,000 - x) = 830
0.04x + 1,400 - 0.07x = 830
-0.03x + 1,400 = 830
-0.03x = 830 - 1,400
-0.03x = -570
x = -570 / -0.03
x = 19,000
Therefore, you invested $19,000 at 4% interest and $20,000 - $19,000 = $1,000 at 7% interest.