Question

If land values stay constant (i.e. i is zero) for the next 3.8 years and the general inflation rate is 4%, by what percentage has the real value of land changed during this time period? Hint: Use the above formula but raise the quotient of the division problem to the appropriate number of years.Make sure to express your final answer as a percentage.

*_t = [{(1 + i_t) / (1 + I_t)} - 1] x 100, where i* = real pre-tax interest rate, i = nominal interest rate, I = annual inflation/growth rate.

Answer 1

As the the land values have remained constant for 3.8 years, therefore nominal growth rate = n = 0% per year

Inflation rate = i = 4% per year, number of years = 3.8 years

Let the real growth rate = r % per year

We know that

r = 0.9615 - 1 = -0.0385 = -3.85% per year

real growth rate of land = -3.85% per year

Real growth rate over 3.8 years = [1 + (-3.85%)]^3.8 -1 = 96.15^3.8 - 1 = 0.8614 - 1 = -0.1386 = -13.86%

Real value of land has decreased by 13.86% over 3.8 years