The amount of annual interest earned by $8000 invested at a certain rate is $200 less than $12,000 would earn at the rate 1% lower. At what rate is the $8,000 invested?
at r%,
8000(r/100) = 12000((r-1)/100) - 200
To find the rate at which the $8,000 is invested, we need to set up an equation based on the information given:
Let's call the rate at which the $8,000 is invested "x" (in decimal form).
According to the question, the amount of annual interest earned by $8,000 at rate "x" is $200 less than what $12,000 would earn at a rate 1% lower than "x".
The interest earned by $8,000 at rate "x" can be calculated using the formula: Interest = Principal * Rate.
So, the interest earned by $8,000 at rate "x" is: Interest1 = 8000 * x.
Now, we need to calculate the rate 1% lower than "x". This can be done by subtracting 1% (0.01) from "x". So, the new rate would be "x - 0.01".
The interest earned by $12,000 at the rate 1% lower than "x" is: Interest2 = 12000 * (x - 0.01).
According to the question, Interest1 (interest earned by $8,000) is $200 less than Interest2 (interest earned by $12,000). Therefore, we can set up the equation:
Interest1 = Interest2 - 200
Substituting the expressions for Interest1 and Interest2:
8000 * x = 12000 * (x - 0.01) - 200
Now, we can solve this equation to find the value of "x", which represents the rate at which the $8,000 is invested.