A total of $5000
is invested: part at 5%
and the remainder at 15%
. How much is invested at each rate if the annual interest is $720
?
Let's assume the amount invested at 5% be x, and the amount invested at 15% be y.
Therefore, according to the given information, we have two equations:
x + y = 5000 ...........(1) (As the total amount invested is $5000)
0.05x + 0.15y = 720 ...........(2) (As the annual interest is $720)
To solve these equations, we can multiply equation (1) by -0.05 and then add it to equation (2):
-0.05x - 0.05y = -250 (multiplying equation (1) by -0.05)
0.05x + 0.15y = 720
By adding these two equations, we get:
0.10y = 470
Dividing both sides of the equation by 0.10, we have:
y = 4700
Now, substitute the value of y back into equation (1) to solve for x:
x + 4700 = 5000
Subtracting 4700 from both sides of the equation, we get:
x = 300
Therefore, $300 is invested at 5% and $4700 is invested at 15%.