suppose you have $12000 to invest. if part is invested 10% and the rest at 15%, how much should be invested at each rate to yield 12% on the total investment?
7,200 at 10% and 4,800 at 15%.
To determine how much should be invested at each rate, we can break down the problem into two equations.
Let's assume that the amount invested at 10% is x dollars, and the amount invested at 15% is 12000 - x dollars (since the rest of the amount is invested at the higher rate).
First, we can calculate the interest earned from each investment:
Interest from the amount invested at 10% = x * 0.10 = 0.10x
Interest from the amount invested at 15% = (12000 - x) * 0.15 = 0.15 * (12000 - x)
To yield a 12% return on the total investment, the total interest earned should be 12% of the total investment:
Total interest = 0.12 * 12000 = 1440
Now, we can set up an equation using the information above:
0.10x + 0.15 * (12000 - x) = 1440
To solve this equation, we can multiply out the terms:
0.10x + 1800 - 0.15x = 1440
Combine like terms:
0.05x + 1800 = 1440
Subtract 1800 from both sides:
0.05x = 1440 - 1800
0.05x = -360
Now, divide both sides by 0.05:
x = -360 / 0.05
x = -7200
Since we cannot invest a negative amount, it seems there is no solution within this situation. Please note that this means it is not possible to achieve a 12% return on the total investment with the given scenario and investment options.
amount invested at 10% --> x
amount invested at 15% --> 12000 - x
solve
.1x + .15(12000-x) = .12(12000)
I suggest multiplying by 100 to get rid of decimals, but not necessary