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You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?

Respuesta :

ogorwyne

The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

How to solve for the amount invested

We have x + y + z = 1000000

((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

4z + x + z = 1000000

((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000

12/100z + 4/100y +2/100z = 34000

2y + 7z = 1700000

-2y - 10z = -2000000

2y + 7z = 1700000

Solve through the use of the simultaneous linear equation

z = 100000

y = 500000

x = 400000

The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

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