Inflation and Real Value

An investment's nominal value is the amount of money recorded. Its real value measures what that money buys in prices from the starting year. With annual inflation \(i\%\), divide the nominal value after \(t\) years by \((1+i/100)^t\).

For principal \(P\), nominal annual interest rate \(R\%\), \(k\) compounding periods per year and annual inflation \(i\%\), \(\text{Real value}=\dfrac{P(1+R/(100k))^{kt}}{(1+i/100)^t}\) after \(t\) years.

Example

With annual investment growth of \(5\%\) and annual inflation of \(3\%\), the annual real growth factor is \(1.05/1.03\), not \(1.02\). After \(t\) years the real value is \(P(1.05/1.03)^t\). Dividing by \((1+i/100)^t\) is the exact method; subtracting the inflation rate from the interest rate is only an approximation, so follow the method a question specifies.

State the assumed constant rates, compounding frequency and time units. Compare like with like: real and nominal balances answer different questions. A model ignores fees, taxes and rate changes unless they are explicitly included.