An investor receives a total of Rs.5,700 per annum in interest from 3 stocks yielding 4%, 5% and 8% per annum respectively. The amount at 4% is Rs.20,000 more than the amount invested at 5%, and the interest from the 8% investment is 8 times the interest from the 5% investment. Amount of money invested in each stock is:
I'm having trouble setting this one up. The one I'm trying to figure out how to lay out in an equation is
Roberto invested some money at 7%, and then invested $5000 more than twice this amount at 9%. His total annual income from the two investments was $3700. How much did he invest at 9%?
I know it would be .07x and .09x, and probably equal to 3700 since it's the output? Should .09 be .09y?
I'm hip when they give the total amount that was invested for the outcome, but this one's throwing me.
thank you for your time.
Let's assume the amount invested at 5% is x.
According to the given information, the amount of money invested at 4% is Rs.20,000 more than the amount invested at 5%. So, the amount invested at 4% is x + Rs.20,000.
The interest earned from the 8% investment is 8 times the interest earned from the 5% investment.
Let's calculate the interest for each investment:
Interest earned from the 4% investment = (4/100) * (x + Rs.20,000) = (4x + 80,000)/100
Interest earned from the 5% investment = (5/100) * x = 5x/100
Interest earned from the 8% investment = (8/100) * x = 8x/100
According to the given information, the total interest earned from all three investments is Rs.5,700. So, we can form the equation:
(4x + 80,000)/100 + 5x/100 + 8x/100 = 5,700
Now, let's solve this equation to find the value of x:
(4x + 80,000 + 5x + 8x)/100 = 5,700
(17x + 80,000)/100 = 5,700
17x + 80,000 = 5,700 * 100
17x + 80,000 = 570,000
17x = 570,000 - 80,000
17x = 490,000
x = 490,000/17
Therefore, the amount invested at 5% is x = 28,823.53 approximately.
The amount invested at 4% is x + Rs.20,000 = 28,823.53 + 20,000 = 48,823.53 approximately.
The amount invested at 8% is 8x/100 = (8 * 28,823.53)/100 = 2,305.88 approximately.
So, the amount of money invested in each stock is as follows:
- Rs.28,823.53 at 5%
- Rs.48,823.53 at 4%
- Rs.2,305.88 at 8%
To find the amount of money invested in each stock, we need to set up a system of equations based on the given information. Let:
- x be the amount invested at 4%,
- y be the amount invested at 5%, and
- z be the amount invested at 8%.
From the given information, we can derive the following equations:
1) The total interest received per annum is Rs. 5,700:
0.04x + 0.05y + 0.08z = 5700
2) The amount at 4% is Rs. 20,000 more than the amount at 5%:
x = y + 20000
3) The interest from the 8% investment is 8 times the interest from the 5% investment:
0.08z = 8 * (0.05y)
Now, let's solve this system of equations to find the values of x, y, and z:
First, let's substitute equation (2) into equation (1) to eliminate x:
0.04(y + 20000) + 0.05y + 0.08z = 5700
0.04y + 800 + 0.05y + 0.08z = 5700
0.09y + 0.08z = 4900 ...........(4)
Next, let's multiply equation (3) by 100 to eliminate decimals:
8z = 8y
Now, substitute 8y for 8z in equation (4):
0.09y + (0.08 * 8y) = 4900
0.09y + 0.64y = 4900
0.73y = 4900
y = 4900 / 0.73
y ≈ 6712.33
Since we have y, we can find the value of x using equation (2):
x = y + 20000
x = 6712.33 + 20000
x ≈ 26712.33
Finally, we can find the value of z by substituting y into equation (3):
8z = 8 * (0.05 * 6712.33)
z = 3356.165
Therefore, the amount invested in each stock is approximately:
x ≈ Rs. 26,712.33
y ≈ Rs. 6,712.33
z ≈ Rs. 3,356.165