An executive invests $29,000, some at 8% and some at 4% annual interest. If he receives an annual return of $1,680, how much is invested at each rate?
.08 x + .04(29,000-x) = 1680
an executive invest 29000, some at 7% and some at 5% annual interest. if he receives an annual return of 1,750 how much is invested at each rate?
13000
To determine how much is invested at each interest rate, let's assign variables to the unknowns.
Let's say the amount invested at 8% is x dollars, and the amount invested at 4% is y dollars.
We are given the following information:
- The total investment amount: x + y = $29,000 (Equation 1)
- The annual return on the investment: 0.08x + 0.04y = $1,680 (Equation 2)
Now, we have a system of equations. We can use these equations to find the values of x and y.
There are several ways to solve this system. One method is to isolate one variable in Equation 1 and substitute it into Equation 2.
From Equation 1, we can isolate x as follows: x = $29,000 - y
Now we substitute this value of x into Equation 2:
0.08($29,000 - y) + 0.04y = $1,680
Multiplying and simplifying, we get:
$2,320 - 0.08y + 0.04y = $1,680
Combining like terms:
-0.04y = $1,680 - $2,320
-0.04y = -$640
Dividing by -0.04 to solve for y:
y = -$640 / -0.04
y = $16,000
Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x = $29,000 - $16,000
x = $13,000
Therefore, $13,000 is invested at 8% and $16,000 is invested at 4%.