Answer:
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
