The nominal interest rate is the amount, in money terms, of interest payable.
For example, suppose a household deposits $100 with a bank for 1 year and they receive interest of $10. At the end of the year their balance is $110. In this case, the nominal interest rate is 10% per annum.
The real interest rate, which measures the purchasing power of interest receipts, is calculated by adjusting the nominal rate charged to take inflation into account.
If inflation in the economy has been 10% in the year, then the $110 in the account at the end of the year buys the same amount as the $100 did a year ago. The real interest rate, in this case, is zero.
After the fact, the 'realized' real interest rate, which has actually occurred, is:
where p = the actual inflation rate over the year.
The expected real returns on an investment, before it is made, are:
= nominal interest rate
= real interest rate
= expected or projected inflation over the year