Suppose 10,000 is invested at 6 percent.how much additional money must be invested at 8 percent to produce a yield on the entire amount invested of 7.2 percent. ( Please show each and every steps of this math with the rough works) THANK YOU SO MUCH.
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To solve this problem, we need to use the concept of weighted averages.
Let's assume the additional amount to be invested at 8% is 'x'.
Step 1: Calculate the interest obtained from the initial investment of $10,000 at 6%.
Interest = Principal * Rate * Time
Interest = 10000 * 0.06 = $600
Step 2: Calculate the interest that needs to be obtained from the additional investment of 'x' at 8%.
Interest = Principal * Rate * Time
Interest = x * 0.08
Step 3: Calculate the weighted average of the interest earned from both investments.
Weighted Average = (Interest1 + Interest2) / Total Principal
7.2% = (600 + 0.08x) / (10000 + x)
Step 4: Solve the equation to find 'x'.
Multiply both sides of the equation by (10000 + x) to eliminate the denominator:
7.2% * (10000 + x) = 600 + 0.08x
720 + 7.2x = 600 + 0.08x
Subtract 0.08x from both sides and subtract 600 from both sides to isolate the 'x' term:
7.2x - 0.08x = 600 - 720
7.12x = -120
Divide both sides by 7.12 to solve for 'x':
x = -120 / 7.12
x ≈ -16.85
Since 'x' represents the additional amount to be invested, it cannot be negative. Therefore, there is no additional amount that can be invested at 8% to produce a yield of 7.2% on the entire investment.
In summary, there is no additional money that must be invested at 8% to produce a yield of 7.2% on the entire amount invested.
add up the interest on each part. It must equal the total interest.
.06(10000) + .08x = .072(10000+x)
x = 15,000
Note that 7.2% is 3/5 of the way from 6% to 8%, and 15000 is 3/5 of the total 25000.