joanna invested $7500, part at a 5.5% and the remainder at a 6% annual rate of interest. if she collected a total of 435 in interest at the end of one year, how much money was invested at each rate?
If x at 5.5%, the rest (7500-x) is at 6%. So, add up the interest:
.055x + .06(7500x) = 435
To find the amounts invested at each rate, we can set up a system of equations based on the given information.
Let's assume Joanna invested x amount of money at a 5.5% annual rate of interest. Therefore, the amount she invested at a 6% rate would be (7500 - x), since the total investment is $7500.
We know that the interest earned on the 5.5% investment is (x * 0.055) and the interest earned on the 6% investment is ((7500 - x) * 0.06). The sum of these interests is equal to $435.
Setting up the equation:
(x * 0.055) + ((7500 - x) * 0.06) = 435
Now we can solve this equation to find the value of x, which represents the amount invested at a 5.5% annual rate.
0.055x + 0.06(7500 - x) = 435
0.055x + 450 - 0.06x = 435
-0.005x = -15
x = 3000
Therefore, Joanna invested $3000 at a 5.5% annual rate of interest. The remaining amount, $4500, was invested at a 6% annual rate.