Kerry earned a total of $900 last year on his investments. If 7000 was invested at a certain rate of return and $9000 was invested in a fund with a rate that was 2% higher, find the two rates of interest.
-Thank you!
7000r + 9000(r+.02) = 900
Well, who knew money could be so interesting? Let's dive in and crunch those numbers for Kerry's investments!
Let's call the rate of return for the $7000 investment "x". So, the interest earned on that investment would be 7000x dollars, right?
Now, the $9000 investment has a rate of interest that is 2% higher than "x", which makes it (x + 0.02). The interest earned on this investment would be 9000(x + 0.02) dollars. Are you still with me?
Since we know Kerry earned a total of $900 in interest, we can set up an equation:
7000x + 9000(x + 0.02) = 900
Now, it's time to solve this equation and find the rates of interest. Let's get those numbers dancing!
Expanding the equation gives us:
7000x + 9000x + 180 = 900
Combining like terms, we get:
16000x + 180 = 900
Subtracting 180 from both sides:
16000x = 720
Finally, dividing both sides by 16000, we find:
x ≈ 0.045
So, the rate of interest for the $7000 investment is approximately 0.045 or 4.5%.
Now, for that $9000 investment with a rate that's 2% higher, we need to add 2% to 4.5%.
2% of 4.5% equals 0.02 * 4.5% = 0.09%. Don't you love math and its calculations?
So, the rate of interest for the $9000 investment is approximately 4.5% + 0.09%, which equals 4.59%.
Voila! The two rates of interest are approximately 4.5% and 4.59%. I hope these numbers put a smile on your face!
Let's say the rate of interest for the investment of $7000 is 'x' percent.
Since the investment of $9000 has a rate that is 2% higher, the rate of interest for this investment will be 'x + 2' percent.
To find the two rates of interest, we can set up an equation using the given information.
The interest earned from the investment of $7000 can be calculated by multiplying the principal ($7000) with the rate of interest ('x') and dividing it by 100:
Interest_1 = (7000 * x) / 100
Similarly, the interest earned from the investment of $9000 can be calculated using the rate of interest ('x + 2'):
Interest_2 = (9000 * (x + 2)) / 100
The total interest earned is given as $900:
Interest_1 + Interest_2 = 900
Substituting the values of Interest_1 and Interest_2, we get:
(7000 * x) / 100 + (9000 * (x + 2)) / 100 = 900
Now, we can solve the equation to find the values of 'x' and 'x + 2'.
Multiplying through by 100 to eliminate the denominators, we have:
7000x + 9000(x + 2) = 90000
Expanding the equation, we get:
7000x + 9000x + 18000 = 90000
Combining like terms, we have:
16000x + 18000 = 90000
Subtracting 18000 from both sides, we get:
16000x = 72000
Dividing by 16000, we find:
x = 4.5
Thus, the rate of interest for the investment of $7000 is 4.5%.
To find the rate for the investment of $9000, we add 2% to the rate:
x + 2 = 4.5 + 2 = 6.5
Therefore, the rate of interest for the investment of $9000 is 6.5%.
Hence, the two rates of interest are 4.5% and 6.5%.
To find the rates of interest on Kerry's investments, we need to set up an equation based on the given information.
Let x be the rate of interest on the first investment of $7000.
Since the second investment of $9000 has a rate that is 2% higher, the rate of interest on this investment would be (x + 2).
The amount earned from the first investment can be calculated using the formula:
Earnings1 = Principal1 * Rate1
Earnings1 = $7000 * x
The amount earned from the second investment can be calculated using the same formula:
Earnings2 = Principal2 * Rate2
Earnings2 = $9000 * (x + 2)
Since the total earnings is given as $900, we can write the equation:
Earnings1 + Earnings2 = $900
$7000 * x + $9000 * (x + 2) = $900
Now we can solve this equation to find the value of x and then calculate the rate of interest on each investment.
$7000x + $9000x + $18,000 = $900
$16,000x + $18,000 = $900
$16,000x = -$17,100
x = -1.07
The negative value for x means that the rate of interest on Kerry's investments is negative, which doesn't make sense in this context. Therefore, there might be an error in the given information or the question.
Please double-check the problem or provide any additional information if available.