If you have ever wondered why your interest rate calculations don’t match those on your credit card or bank statement it may be because of the difference between real interest rates and nominal interest rates. This difference between interest rates is the inclusion of an inflation adjustment in the interest rate. Inflation in this usage of the word, is reduction in the value of money over time. However, this should not be confused with ‘inflation adjusted securities’ which add rather than subtract the rate of inflation. Real interest rates are ‘real’ because they deduct inflation whereas nominal interest rates do not. It’s not quite so simple however, as both nominal and real interest rates may also be compounded.
Interest rates can be deceptive because there are so many ways to calculate interest. To name a few, there are Annual Percentage Rates (APR), compounded interest rates, nominal interest rates, Effective Interest Rates (EIR) which use compounded interest in their calculation, and real interest rates. These interest rates may be either fixed or variable. Being aware of if your quoted interest rate is real or nominal in addition to the difference between these interest rates can be helpful in determining if you’re really getting a deal on something instead of what just seems to be a deal.
HOW TO CALCULATE NOMINAL AND REAL INTEREST:
• Nominal interest calculation
The difference between nominal and real interest rates can also be illustrated in the calculations of the various forms of nominal and real interest rates. For example, calculating non-compounded nominal interest is the most conventional form of interest rate calculation and simply involves multiplying the amount by the interest rate i.e. $100 x 5% or .05 = $5. This $5 is not compounded however, and compounding interest is quite common in financial institutions.
• Compounded nominal interest
If the 5% is compounded monthly, the resulting balance will be more than $105 because of the compounding. For example the same $100 compounded monthly at a nominal interest rate for one year would be calculated by dividing $5 by 12 for .4166 cents first months interest. This .4166 cents is added to the $100 at the end of the first month for a balance of $100.4166. The second month’s interest rate is then calculated using the same process, but with the new balance.
• Real interest rate calculation
Using the same example as above, a real interest rate deducts the rate of inflation from the nominal interest rate. Depending on the financial instrument, real interest rates may be adjusted monthly, bi-annually or periodically. For example, if the rate of inflation is recorded as 2% by the Federal Reserve Bank, and this is the rate used in calculating real interest rates, then 5%-2%=3% making the real interest rate 3%. If the real interest rate is calculated quarterly, i.e. every 3 months, this rate can change 4 times a year.
• Compounded real interest
Like nominal interest rates, real interest rates can also be compounded. The only difference between fixed compounded real interest rates and fixed nominal interest rates is the interest rate is likely to be lower for real interest rates. For example, using the $100 from above, the actual interest rate used is 3% not 5% so the first month’s interest rate is calculated by multiplying $100 by .03 or 3% for an annual interest rate of $3 divided by 12 for .25 cents applied to the first month and 3% then applied to the balance of $100.25 and then divided by 12 for the second month’s compounded interest.
FIXED VS VARIABLE NOMINAL AND REAL INTEREST RATES
Both real and nominal interest rates can also be fixed or variable. Fixed means the interest rate does not change and variable means the interest rate does change. When applied to nominal and real interest rates, no change to computing the above interest takes place if the interest rate is fixed. However, if the rate is variable, the rate of interest that is used when compounding varies.
To illustrate the affect of variable rates using the $100 from above both nominal and real interest can result in a difference from the first month and second month’s interest. If the first month’s interest is .25 cents but then the real interest rate is adjusted to 3.5% then the second month would be calculated by multiplying $100.25 by 3.5% or .035 and then dividing that amount by 12 for the second months interest i.e. $100.25 x .035= .2923 cents. If the rate had not been variable, the second month’s interest rate would be the same as the example of compounded real interest above i.e. $100.25 x .03 =.2506.
Source: http://www.investopedia.com (Investopedia)