A person invests $4500.oo into 2 different mutual funds. The first has a 4.5% interest rate the second 6%. He made a total of $225 in the investment. How much did he invest in each fund?
Invested $X @ 4.5%.
Invested $(4500-X) @ 6%.
Investment assumed to be for 1 year.
.045x + 0.06(4500-x) = $225.
.045x + 270 - 0.06x = 225
-0.015x = 225 - 270 = -45
X = $3000 @ 4.5%.
4500-x = 4500-3000 = $1500 @ 6%.
To find out how much the person invested in each fund, let's assign variables to the unknowns.
Let's say the amount invested in the first fund is x dollars, and the amount invested in the second fund is y dollars.
According to the given information, the total investment amount is $4500, so we have the equation:
x + y = 4500
Now, let's calculate the interest earned from each fund.
The interest earned from the first fund can be calculated by multiplying the amount invested (x) by the interest rate (4.5%) and dividing it by 100:
Interest from first fund = (x * 4.5) / 100
Similarly, the interest earned from the second fund can be calculated as:
Interest from second fund = (y * 6) / 100
The total interest earned from both funds is given as $225. So, we can write another equation:
Interest from first fund + Interest from second fund = 225
Substituting the previously calculated values, we have the equation:
((x * 4.5) / 100) + ((y * 6) / 100) = 225
Now, we have a system of equations:
1) x + y = 4500
2) ((x * 4.5) / 100) + ((y * 6) / 100) = 225
To solve this system, we can use substitution or elimination methods.
Let's solve it using the substitution method:
From equation 1), we have x = 4500 - y
Substituting this into equation 2):
((4500 - y) * 4.5) / 100 + ((y * 6) / 100) = 225
Expanding and simplifying:
(20250 - 4.5y + 6y) / 100 = 225
(20250 + 1.5y) / 100 = 225
Cross-multiplying:
20250 + 1.5y = 22500
1.5y = 22500 - 20250
1.5y = 2250
Dividing both sides by 1.5:
y = 1500
Substituting this value back into equation 1) to find x:
x + 1500 = 4500
x = 4500 - 1500
x = 3000
Therefore, the person invested $3000 in the first fund and $1500 in the second fund.