Question

You would like to purchase a vacation home in 10 years. The current price of such a home is $500,000 but the price of these types of homes is rising at a rate of 3% per year. How much would you have to invest today in nominal terms to exactly pay for the vacation home if your investments earn 5% APR (compounded annually) in nominal terms?

Answer 1

$412,524.038

Step-by-step explanation:

Given:

Time duration, n = 10 years

Present value of the home = $500,000

Rate of interest = 3% per year = 0.03

APR = 5%

Now,

The future value of the home :

Future value = Present value × ( 1 + r )ⁿ

on substituting the respective values, we get

Future value = $500,000 × ( 1 + 0.03 )¹⁰

or

Future value = $671,958.19

Therefore,

The amount invested (P) will be

$671,958.19 = P × ( 1 + 0.05 )¹⁰

or

$671,958.19 = P × 1.63

Or

P = $412,524.038