A women has $500,000 invested in two rental properties. One yields an annual return of 14% on her investment, and the other returns 10% per year on her investment. Her total annual return from the two investments is $59,000. How much is invested at each return?
A + B = 500,000
.14 A + .10 B = 59,000
multiply second equation by 10
1.0 A + B = 500,000
1.4 A + B = 590,000
--------------------- subtract
-.4 A = -90,000
A = 225,000 etc
Thanks Damon!
You are welcome.
To determine how much is invested at each return, you can set up a system of equations based on the given information.
Let's say x is the amount invested in the property with a 14% return, and y is the amount invested in the property with a 10% return.
According to the problem, the total invested amount is $500,000:
x + y = $500,000 Equation 1
The annual return from the property with a 14% return is 14% of x:
0.14x
The annual return from the property with a 10% return is 10% of y:
0.10y
The total annual return from both investments is $59,000:
0.14x + 0.10y = $59,000 Equation 2
Now, you need to solve this system of equations.
One way to do this is by substitution. Solve Equation 1 for x and substitute it into Equation 2:
x = $500,000 - y
0.14($500,000 - y) + 0.10y = $59,000
Expand and simplify:
$70,000 - 0.14y + 0.10y = $59,000
Combine like terms:
$70,000 - $59,000 = 0.14y - 0.10y
$11,000 = 0.04y
Divide both sides by 0.04:
$11,000 / 0.04 = y
y = $275,000
Now substitute the value of y back into Equation 1 to find x:
x + $275,000 = $500,000
x = $500,000 - $275,000
x = $225,000
Therefore, $225,000 is invested in the property with a 14% return, and $275,000 is invested in the property with a 10% return.