and investor has a total of $24,900 deposited in three different accounts which earn annual interest rate of 7% 6% and 4%. the amount deposited in the 7% account is twice the amount in the 6% account. if the three accounts earn a total annual interest of $1412 how much money is deposited each account
similar to your other question
let the amount invested at 6% be x
then the amount at 7% is 2x
let the amount invested at 4% be y
so x + 2x + y = 24900
y = 24900 - 3x
.06x + .07(2x) + .04(24900-3x) = 1412
proceed as before
To solve this problem, let's assign variables to represent the amounts deposited in each account.
Let's say:
- The amount deposited in the 7% account is x.
- The amount deposited in the 6% account is y.
- The amount deposited in the 4% account is z.
Given that the total amount deposited is $24,900, we can create an equation:
x + y + z = 24,900 ----(1)
It is also stated that the amount deposited in the 7% account is twice the amount in the 6% account, so we can create another equation:
x = 2y ----(2)
Now, let's calculate the interest earned for each account:
Interest earned from the 7% account = x * 7/100 = 0.07x
Interest earned from the 6% account = y * 6/100 = 0.06y
Interest earned from the 4% account = z * 4/100 = 0.04z
Given that the total interest earned is $1412, we can create another equation:
0.07x + 0.06y + 0.04z = 1412 ----(3)
We now have a system of three equations (equations 1, 2, and 3) with three variables (x, y, and z). We can solve this system to find the values of x, y, and z.
Substituting equation (2) into equation (1), we get:
2y + y + z = 24,900
3y + z = 24,900 ----(4)
Now, we can substitute equations (2) and (4) into equation (3):
0.07(2y) + 0.06y + 0.04z = 1412
0.14y + 0.06y + 0.04z = 1412
0.20y + 0.04z = 1412 ----(5)
Now, we have a system of two equations (equations 4 and 5) with two variables (y and z). We can solve this system to find the values of y and z.
To solve this system of equations, we can use the substitution method, elimination method, or any other preferred method.
Once we find the values of y and z, we can substitute them back into equation (2) to find the value of x.
I hope this explanation helps you understand how to approach this problem!