Question

How many years will it take to decrease the purchasing power of a dollar by half if the inflation rate is 4% indefinitely?

Answer 1

Purchasing power of a dollar is defined as 100/P, where P is the price index of that year.

Lets say, initially, P = $1

Purchasing power of dollar initially = 100/1 = 100

For purchasing power to be half ( = 50), P = $2. This implies that due to inflation the one dollar has appreciated to become two dollars.

Final Value = Initial Value × ( 1 + inflation rate)ⁿ , where n is the number of years

Final Value = $2

Initial Value = $1

Inflation rate = 4% = 0.04

∴ 2 = 1 × (1 + 0.04)ⁿ

Taking log on both sides:

log 2 = n log(1.04)

n = (log 2)/(log 1.04) = 17.67 years