A woman involved a sum money 8890 partly at 10percent and partly at 15percent if the total interest is 560 per annum find the amount invested at 15percent
10% gives $889 after one year.
15% gives $8890*0.15=$1333.5 after one year.
So the annual interest is a minimum of $889.
If only $560 was earned after one year, someone got short-changed, sorry to say.
To find the amount invested at 15%, we would need to set up two equations using the given information.
Let's assume the amount invested at 10% is x. Therefore, the amount invested at 15% would be (8890 - x) since the total amount invested is 8890.
We can now set up the equations using the formula for calculating simple interest:
Interest = (Principal * Rate * Time)
For the amount invested at 10%:
Principal = x
Rate = 10% = 0.10
Interest = (x * 0.10 * 1) (assuming 1 year)
For the amount invested at 15%:
Principal = 8890 - x
Rate = 15% = 0.15
Interest = [(8890 - x) * 0.15 * 1] (assuming 1 year)
Given that the total interest is 560 per annum:
(x * 0.10 * 1) + [(8890 - x) * 0.15 * 1] = 560
Now, we can solve this equation to find the value of x and then calculate the amount invested at 15%.
Let's simplify the equation:
0.10x + 0.15(8890 - x) = 560
0.10x + 1333.5 - 0.15x = 560
-0.05x = -773.5
x = 773.5 / 0.05
x ≈ 15,470
Therefore, the woman invested approximately 15,470 at 10% and (8890 - 15470) = -6,580 at 15%. Note that a negative value indicates that there was no investment at 15%.