Larry has an annual return of $213.00 from $3000.00 invested at simple interest. One at 5% and the other at 8%. How much is invested at each rate. (Hint, Interest earned = amount invested x rate of interest.)
.05x + .08(3000-x) = 213.00
x=900
so, $900 at 5% and $2100 at 7%
To find out how much was invested at each rate, let's solve the problem step by step.
Let's assume Larry invested x dollars at 5% interest and y dollars at 8% interest.
According to the hint, we can use the formula: Interest earned = amount invested × rate of interest.
For the investment at 5% interest, the interest earned is: 0.05x
For the investment at 8% interest, the interest earned is: 0.08y
The total interest earned is given as $213.00, so we can create an equation:
0.05x + 0.08y = 213 (Equation 1)
The total amount invested is $3000.00, so we can create another equation:
x + y = 3000 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y).
We can solve these equations to find the values of x and y.
Let's start by isolating one of the variables in Equation 2:
x = 3000 - y
Now, substitute this value of x into Equation 1:
0.05(3000 - y) + 0.08y = 213
Simplify and solve for y:
150 - 0.05y + 0.08y = 213
0.03y = 63
Divide both sides by 0.03:
y = 63 / 0.03
y = 2100
Now that we have found the value of y, we can substitute it back into Equation 2 to find x:
x + 2100 = 3000
x = 3000 - 2100
x = 900
Therefore, Larry invested $900 at 5% interest and $2100 at 8% interest.