An investor must invest a total of $15,000 in two accounts, one paying 4% annual interest, and the other 3%. If he wants to earn $550 annual interest, how much should he invest at each rate?
.04x + .03(15000-x) = 550
To determine how much the investor should invest at each interest rate, we can set up a system of equations.
Let's assume the investor invests x dollars at 4% interest, and y dollars at 3% interest.
According to the problem, the investor must invest a total of $15,000, so we have our first equation:
x + y = 15,000
The investor wants to earn $550 in annual interest, so we have our second equation:
0.04x + 0.03y = 550
Now we have a system of equations:
x + y = 15,000
0.04x + 0.03y = 550
There are various methods to solve systems of equations, but let's use the substitution method here.
We can solve the first equation for x:
x = 15,000 - y
Now we substitute this expression for x in the second equation:
0.04(15,000 - y) + 0.03y = 550
Distribute 0.04:
600 - 0.04y + 0.03y = 550
Combine like terms:
0.03y - 0.04y = 550 - 600
-0.01y = -50
Multiply both sides by -100 to isolate y:
y = (-50) * (-100)
y = 5000
Now substitute this value for y into the first equation:
x + 5000 = 15,000
Solve for x:
x = 15,000 - 5000
x = 10,000
Therefore, the investor should invest $10,000 at 4% interest and $5,000 at 3% interest to earn $550 in annual interest.