Question

A farmer bought a scratch ticket and found out later that he won $1,800,000. After 30% was deducted for income taxes he invested the rest; some at 4.75% and some at 6.25%. If the annual interest earned from his investments is $72,135, find the amount he invested at each rate.

Answer 1

The amount invested in the investment that yields an interest rate of 4.75% is $441,000.

The amount invested in the investment that yields an interest rate of 6.25% is $819, 000.

What is the income tax paid by the farmer?

Income tax is the tax levied by the government on the income of individuals or companies.

Income tax = tax rate x income

30% x $1,800,000

= 0.3 x $1,800,000.

= $540,000

After tax income = $1,800,000 - $540,000 = $1,260,000

System of equations that can be determined from the question

a + b = $1,260,000 equation 1

0.0475a + 0.0625b = $72,135 equation 2

Where:

a = amount invested in the investment that yields an interest rate of 4.75%

b = = amount invested in the investment that yields an interest rate of 6.25%

What is the value of b?

In order to determine the value of b, take the following steps:

Multiply equation 1 by 0.0475

0.0475a + 0.0475b = 59,850 equation 3

Subtract equation 3 from equation 2

12,285 = 0.015b

Divide both sides of the equation by 0.015

b = $819, 000

What is the value of a?

a + $819,000 = $1,260,000

a = $1,260,000 - $819,000

a = $441,000

Explanation:

Hii this is not my answer this was from another same question you asked but i hope this helps ^^