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

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

Explanation:

Amount required for property taxes is given as

Amount required
`= (Property\ taxes\ in\ year\ 6)/((Interest\ rate - Growth\ rate))`

where Porperty tax = $500,000

interest tax = 10%

growth rate = 1%

`= (500,000)/((10\% - 1\%))`

= 5,555,556

Thus, the amount required after 5 years property taxes is $5,555,556.

So, Present value

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

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