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Linda won $200,000 in a state lottery. She first paid income tax on 30% on the winnings. She invested some of the rest at 1.5% and some at 4%, earning $4350 interest per year. How much did she invest at each rate?

Respuesta :

She invested $ 50000 at 1.5% rate and $ 90000 at 4% rate.

Explanation

Total amount of winnings = $ 200000

She first paid income tax on 30% on the winnings. So, the amount paid as income tax [tex]=(200000*0.30)dollar=60000[/tex] dollar.

Remaining amount = $ 200000 - $ 60000 = $ 140000

Suppose, she invested  [tex]x[/tex] dollar at 1.5% rate.

That means, she invested [tex](140000-x)[/tex] dollar at 4% rate.

Given that, the total amount of interest earned = $ 4350

So, the equation will be.....

[tex]0.015x+0.04(140000-x)=4350\\ \\ 0.015x+5600-0.04x=4350\\ \\ -0.025x= 4350-5600\\ \\ -0.025x=-1250\\ \\ x= \frac{-1250}{-0.025}=50000[/tex]

So, amount of investment at 1.5% rate = $ 50000

and amount of investment at 4% rate = $ 140000 - $ 50000 = $ 90000  


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