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24 September, 05:52

Question

Vartan was paid $25,000 for a cell phone app that he wrote and wants to invest it to save for his son's education. He wants

to put some of the money into a bond that pays 4% annual interest and the rest into stocks that pay 9% annual interest. If

he wants to earn 7.4% annual interest on the total amount, how much money should he invest in each account?

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Answers (1)
  1. 24 September, 08:38
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    The money invested into bond is $8000

    The money invested into stocks is $17,000

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Vartan wants to invest $25,000

    - He wants to put some of the money into a bond that pays 4% annual

    interest and the rest into stocks that pay 9% annual interest

    - He wants to earn 7.4% annual interest on the total amount

    - We need to know how much money he should invest in each account

    - Assume that he will put $x into the bond that pays 4% annual interest

    - He will put the rest into stocks that pay 9%

    - The rest = 25,000 - x

    ∴ The money earns = (4/100) (x) + (9/100) (25,000 - x)

    ∴ The money earns = 0.04 x + 2250 - 0.09 x

    ∴ The money earns = 2250 - 0.05 x ⇒ (1)

    ∵ He wants to earn 7.4% annual interest on the total amount

    ∵ Total amount is $25,000

    ∴ The money earns = (7.4/100) (25,000)

    ∴ The money earns = 1850 ⇒ (2)

    - Equate (1) ans (2)

    ∴ 2250 - 0.05 x = 1850

    - Add 0.05 x to both sides

    ∴ 2250 = 0.05 x + 1850

    - Subtract 1850 from both sides

    ∴ 400 = 0.05 x

    - Divide both sides by 0.05

    ∴ x = 8,000

    ∴ 25,000 - 8,000 = 17,000

    ∵ x represents the money invested into the bond

    ∵ 25,000 - x represents the money invested into the stocks

    ∴ The money invested into bond is $8000

    ∴ The money invested into stocks is $17,000
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