Question

Assume Courtney decides to purchase Intel stock for $100,000. She plans to hold half the shares for 5 years to purchase the Park City home and hold the other half for 8 years to pay for Deron's education. If the Intel stock grows at a constant 8% before-tax rate and does not pay any dividends, how much cash will Courtney accumulate after taxes for the Park City home?

Answer 1

Using the formula for compound interest, Courtney would accumulate approximately $73,466.50 before taxes for the Park City home by investing $50,000 at an 8% growth rate for 5 years.

Step-by-step explanation:

Calculating Investment Growth After Taxes

When Courtney invests $100,000 in Intel stock and plans to sell half of the shares to purchase a home after 5 years, the growth can be calculated using the formula for compound interest. Assuming an 8% growth rate and no dividends, the equation to calculate the future value FV is: FV = P(1 + r)^n, where P is the principal amount ($50,000, since she's holding half for the Park City home), r is the annual interest rate (0.08), and n is the number of years (5).

To find the amount after taxes, we should subtract the taxes due from the future value. However, since the question does not specify the tax rate, we'll calculate the pre-tax amount:

FV = $50,000(1 + 0.08)^5

Using a calculator, this comes out to:

FV = $50,000(1.08)^5

FV = $50,000(1.46933)

FV ≈ $73,466.50 (before tax)

This would be the amount Courtney has accumulated before taxes for the Park City home.