Question

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?

Answer 1

Linda invested $40,000 at 1.5% and $100,000 at 4%.

Step-by-step explanation:

To determine how much Linda invested at each rate, we can set up a system of equations based on the given information. Let's assume she invested x dollars at 1.5% and y dollars at 4%.

From the question, we know that the total interest earned from these investments is $4350.

The interest earned from the investment at 1.5% is then 0.015x, and the interest earned from the investment at 4% is 0.04y.

Summing these two interest amounts gives us the equation 0.015x + 0.04y = 4350.

We also know that Linda won $200,000 in the lottery and paid income tax of 30% on the winnings.

After paying taxes, she invested the rest. So, the amount she invested can be found by subtracting 30% of $200,000 from $200,000. This gives us (1-0.3) * $200,000 = 0.7 * $200,000 = $140,000.

Finally, we can set up a second equation using the fact that the total amount Linda invested is the sum of her investments at the two interest rates. This gives us x + y = $140,000.

Now, we have a system of equations:

0.015x + 0.04y = 4350 (equation 1)

x + y = $140,000 (equation 2)

We can solve this system of equations to find the values of x and y.

By solving the system, we find that x = $40,000 and y = $100,000.

Therefore, Linda invested $40,000 at 1.5% and $100,000 at 4%.

Answer 2

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
`=(200000*0.30)dollar=60000` dollar.

Remaining amount = $ 200000 - $ 60000 = $ 140000

Suppose, she invested
`x` dollar at 1.5% rate.

That means, she invested
`(140000-x)` dollar at 4% rate.

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

So, the equation will be.....

`0.015x+0.04(140000-x)=4350\\ \\ 0.015x+5600-0.04x=4350\\ \\ -0.025x= 4350-5600\\ \\ -0.025x=-1250\\ \\ x= (-1250)/(-0.025)=50000`

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

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