Question

You are told today that you’ll inherit a castle from your uncle in 5 years. You’ll need to

pay a property tax of $500,000 on the castle in year 6. Then the property tax will go up

each year by 1%. You and your descendant are going to pay for the property tax each year

forever. Suppose the interest rate is 10% per year. If you want to set aside enough money

today to be able to make all the future property tax payment, how much money do you

need?

Answer 1

Compute the amount set aside after 5 years from now for property taxes, using the equation as shown below:

Amount required = Property taxes in year 6/ (Interest rate – Growth rate)

                            = $500,000/ (10% - 1%)

                            = 5,555,556

Hence, the amount required after 5 years from now for property taxes is $5,555,556.

Compute the amount set aside today for property taxes, using the equation as shown below:

Present value = Amount required after 5 years/ (1 + Rate)^{Number of years}

                     = $5,555,556/ (1 + 0.10)⁵

                     = $5,555,556/ 1.6105

                      = $3,449,563

Hence, the amount set aside today for property taxes is $3,449,563.