# Inflation

Updated 2018-08-08

# Inflation

**Inflation** is the rise of prices of goods and services (reduction in purchasing power) over time.

Inflation rate can apply to:

**individual items**: an orange today costs $0.69 costs $0.64 last year; the inflation rate is 7.8%**commodity**: inflation rate of bread is taken from average prices**basket of goods**: general consumer prices

Example: average inflation rateGiven the base price of $100 in year 0, inflation rate in year 1 is 5%, year 2 is 3%, what is average inflation rate over two years?

First, find the

\[100(1+0.05)(1+0.03)=108.15\]realprice at the end of year 2:Then take average inflation rate \(f\) which is constant and plug it into the equation:

\[100(1+f)^n=108.15\]where \(n=2\) for 2 years. \(f=3.995\%\).

## Definitions

**Inflation Rate**(\(f\)): annual rate of increase of cost to the same goods and services**Real Interest Rate**(\(i_R\) or \(i'\)):*real*growth of money (:x:**excluding**effect of inflation)**Real / Constant Dollars**($R$$ or \(R_N\)): dollar with constant purchasing power, expressed using base year (:x:**excluding**inflation)**Nominal / Market Interest Rate**(\(i\)): rate that one obtains in general market place (:white_check_mark:**includes**inflation and real interest)**Nominal / Actual Dollars**($A$$ or \(A_N\)): money at face-value

The relationship between real and nominal interest rate is:

\[(1+i)=(1+i')(1+f)\]The relationship between real and nominal dollar is:

\[R_N=\frac{A_N}{(1+f)^N}\]or simply:

\[R_N=A_N(P/F, f, N)\]