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You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 5 %

compounded annually, the second account pays 2 % compounded annually, and the third account pays 3 %

compounded annually. After one year, you earn $36250 in interest. If you invest four times the money into the

account that pays 5 % compared to 3 % , how much did you invest in each account?

5 %:$

2%:$

3 %:$

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J

2)

Respuesta :

sqdancefan

Answer:

  • 5%: $500,000
  • 2%: $375,000
  • 3%: $125,000

Step-by-step explanation:

Let x, y, z represent the amounts invested in the first, second, and third accounts. The given relations are ...

  x + y + z = 1,000,000

  .05x +.02y +.03z = 36,250

  x - 4z = 0

__

Your calculator can tell you the solution to these equations is ...

  x = $500,000 . . . amount invested at 5%

  y = $375,000 . . . amount invested at 2%

  z = $125,000 . . . amount invested at 3%

_____

The attached graphing calculator screenshot shows one way this can be solved using a system of 2 equations in x and y. (X- and y-values are in thousands.)

An equally good substitution would be for x: x = 4z. Then you would have two equations in y and z:

  y + 5z = 1,000,000

  0.02y +0.23z = 36,250

The solution to these by any of your favorite methods is ...

  (y, z) = (375000, 125000) and x=4z = 500000

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