A banker invested money in two investments. The first investment returned 4% simple interest. The second investment returned 12% simple interest. If the second investment had $260.00 more money than the first, and the total interest for both investments was $133.60, find the amount invested in each investment.
(m * .04) + [(m + 260) * .12] = 133.60
.04 m + .12 m + (.12 * 260) = 133.60
Why did the banker always carry a calculator? Because he was always calculating his investments! Now let's crunch the numbers and solve this finance puzzle.
Let's say the amount invested in the first investment is x dollars. Therefore, the amount invested in the second investment would be (x + $260).
The interest earned from the first investment at 4% simple interest can be calculated as 0.04x.
The interest earned from the second investment at 12% simple interest can be calculated as 0.12(x + $260).
Now, we know that the total interest for both investments is $133.60. So we can set up the equation:
0.04x + 0.12(x + $260) = $133.60
Simplifying the equation, we get:
0.04x + 0.12x + $31.20 = $133.60
Combining like terms, we have:
0.16x + $31.20 = $133.60
Subtracting $31.20 from both sides:
0.16x = $133.60 - $31.20
0.16x = $102.40
Dividing both sides by 0.16:
x = $102.40 / 0.16
x = $640
So the amount invested in the first investment is $640, and the amount invested in the second investment is $640 + $260 = $900.
In conclusion, the banker invested $640 in the first investment and $900 in the second investment.
Let's assume the amount invested in the first investment is x dollars.
According to the question, the second investment had $260.00 more than the first investment. So, the amount invested in the second investment is (x + $260.00).
The interest earned from the first investment is given by:
Interest_1 = (x * 4%) = 0.04x
The interest earned from the second investment is given by:
Interest_2 = [(x + $260.00) * 12%] = 0.12(x + $260.00)
According to the question, the total interest from both investments is $133.60. So, we can set up the equation:
Interest_1 + Interest_2 = $133.60
0.04x + 0.12(x + $260.00) = $133.60
Simplifying the equation:
0.04x + 0.12x + 0.12($260.00) = $133.60
0.16x + $31.20 = $133.60
Subtracting $31.20 from both sides:
0.16x = $133.60 - $31.20
0.16x = $102.40
Dividing both sides by 0.16:
x = $102.40 / 0.16
x ≈ $640.00
Therefore, the amount invested in the first investment is approximately $640.00.
And the amount invested in the second investment is:
x + $260.00
$640.00 + $260.00
≈ $900.00
So, the amount invested in the second investment is approximately $900.00.
To find the amount invested in each investment, let's use the following steps:
Step 1: Assign variables to the unknowns:
Let's say the amount invested in the first investment is x dollars.
Therefore, the amount invested in the second investment would be x + $260.00, as it had $260.00 more than the first investment.
Step 2: Calculate the interest for each investment:
The interest for the first investment at a 4% simple interest rate can be calculated as:
Interest1 = (4/100) * x
The interest for the second investment at a 12% simple interest rate can be calculated as:
Interest2 = (12/100) * (x + $260.00)
Step 3: Set up the equation:
Since the total interest for both investments is given as $133.60, we can set up the equation as follows:
Interest1 + Interest2 = $133.60
Step 4: Solve the equation:
Substitute the calculated values of Interest1 and Interest2 into the equation:
(4/100) * x + (12/100) * (x + $260.00) = $133.60
We can now simplify and solve this equation to find the value of x and then calculate the amount invested in each investment.