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

Answer:

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

Step-by-step explanation:

Amount required for property taxes is given as

Amount required $= \frac{Property\ taxes\ in\ year\ 6}{(Interest\ rate - Growth\ rate)}$

where Porperty tax  = $500,000

interest tax = 10%

growth rate  =  1%

                           $= \frac{500,000}{(10\% - 1\%)}$

                           = 5,555,556

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

So, Present value

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

                    $= \frac{5,555,556}{(1 + 0.10)^5}$

                    $= \frac{5,555,556}{1.6105}$

                    = $3,449,563

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