John has $6000 to invest. He invests part of it at 5% and the rest at 8%.How much should be invested at each rate to yield 6% on the total amount?
$X @ 5%
$(6000-x) @ 8%
0.05x + 0.08(6000-x) = 0.06*6000
Multiply both sides by 100:
5x + 8(6000-x) = 6*6000
Solve for x.
X=4000
To solve this problem, let's assume John invests $x at 5% interest and the remaining amount ($6000 - x) at 8% interest. We need to find the values of x and ($6000 - x) that will yield a 6% return on the total investment.
First, let's calculate the interest earned from the $x investment at 5%. The formula for calculating simple interest is:
Interest = Principal × Rate × Time
Let's assume John invests the money for one year. Therefore, the interest earned from the $x investment at 5% is:
Interest_5% = x × 0.05 × 1
Next, let's calculate the interest earned from the ($6000 - x) investment at 8%. Using the same formula, we have:
Interest_8% = ($6000 - x) × 0.08 × 1
We want the total interest from both investments to be equal to 6% of the total investment:
Total_Interest = Interest_5% + Interest_8%
Since Total_Interest should be equal to 6% of the total investment, we have:
0.06 × Total_Investment = Interest_5% + Interest_8%
0.06 × 6000 = x × 0.05 + ($6000 - x) × 0.08
Now, we can solve this equation to find the value of x:
360 = 0.05x + 480 - 0.08x
Combining like terms, we simplify to:
360 = -0.03x + 480
Rearranging the equation:
0.03x = 480 - 360
0.03x = 120
Dividing both sides by 0.03:
x = 120 / 0.03
x = 4000
So, John should invest $4000 at 5% interest and ($6000 - $4000) = $2000 at 8% interest to yield a 6% return on the total investment.