a total of 10,000 is invested in two mutual funds. the first account yields 5% and the second account yields 6%. how much is invested in each account if the interest in a year in $575?
i don't know if m supposed to add or not with the %
If $x is at 5%, then the rest (10000-x) is at 6%. The interest of both parts must add up to 575:
.05x + .06(1000-x) = 575
To solve this problem, let's assume that x amount is invested in the first mutual fund (yielding 5%) and the remaining amount (10,000 - x) is invested in the second mutual fund (yielding 6%).
The interest earned from the first fund is calculated as 5% of x, or 0.05x.
The interest earned from the second fund is calculated as 6% of (10,000 - x), or 0.06(10,000 - x).
According to the problem, the total interest earned is $575. Therefore, we can write the equation:
0.05x + 0.06(10,000 - x) = 575
Simplifying the equation:
0.05x + 600 - 0.06x = 575
-0.01x = -25
x = 2500
So, $2500 is invested in the first mutual fund (yielding 5%) and (10,000 - 2500) = $7500 is invested in the second mutual fund (yielding 6%).
To find out how much is invested in each account, we can use a system of equations. Let's denote the amount invested in the first account as "x", and the amount invested in the second account as "y".
We know that the total amount invested is $10,000. So, our first equation is:
x + y = 10,000
The interest earned from the first account is 5% of the amount invested (0.05x), and the interest earned from the second account is 6% of the amount invested (0.06y). The total interest earned is $575. So our second equation is:
0.05x + 0.06y = 575
To solve this system of equations, we can multiply the first equation by 0.05 to eliminate the term "x" when we add the two equations together:
0.05x + 0.05y = 0.05 * 10,000
0.05x + 0.06y = 575
Now we have a new system of equations:
0.05x + 0.05y = 500
0.05x + 0.06y = 575
Subtracting the two equations:
(0.05x + 0.06y) - (0.05x + 0.05y) = 575 - 500
0.01y = 75
Dividing both sides by 0.01:
y = 75 / 0.01
y = 7500
Now we know that the amount invested in the second account (y) is $7500. To find out the amount invested in the first account (x), we can substitute y back into the first equation:
x + 7500 = 10,000
x = 10,000 - 7500
x = 2500
Therefore, $2500 is invested in the first account and $7500 is invested in the second account.