Real Interest Rates and the Fisher Effect.

Consider a one-year loan contract. Adam lends Beth \$500, and Beth promises to repay Adam \$550 next year. The nominal or money rate of interest is clearly ten percent.

Nominal rate of interest = amount of money repaid - amount of money lent / amount of money lent

The real rate of interest is defined in similar terms; however, we look at the amount of goods repaid and lent:

Real rate of interest = amount of goods repaid - amount of goods lent / amount of goods lent

If you lend 100 bushels of apples and receive 105 bushels of apples next year, the real rate of interest is five percent. Now, it is very rare to actually write loan contracts in terms of goods. The real rate of interest studied in macroeconomics reflects how much the money amounts lent and repaid would buy in terms of goods.

The following examples assume that the money rate of interest is 10 percent; that \$500 is lent, and \$550 repaid. The quantity of apples for the next year is always computed as \$550 / Pa, where Pa is the price of apples next year.

Now Next Year

Money lent/repaid          \$500                  \$550 Nominal rate of interest = 10 percent

Price of apples               \$ 5                     \$ 5                     Inflation rate = 0 percent

Quantity of apples         100 bushels       110 bushels Real rate of interest = 10 percent

bought

Price of apples               \$ 5                     \$5.10                 Inflation rate = 2 percent

Quantity of apples         100 bu.              108 bu.              Real rate of interest = 8 percent

Price of apples               \$ 5                     \$5.20                 Inflation rate = 4 percent

Quantity of apples         100 bu.              106 bu.              Real rate of interest = 6 percent.

Price of apples               \$ 5                     \$5.40                 Inflation rate = 8 percent

Quantity of apples         100 bu.              102 bu.              Real rate of interest = 2 percent

Price of apples               \$ 5                     \$5.50                 Inflation rate = 10 percent

Quantity of apples         100 bu.              100 bu.              Real rate of interest = 0 percent

Price of apples               \$ 5                     \$5.60                 Inflation rate = 12 percent

Quantity of apples         100 bu.              98 bu.                Real rate of interest = minus 2 percent

Note that these calculations all fit the formula of the text:

Real rate of interest = nominal rate of interest minus the inflation rate

Note also that the calculations are rounded off; for example, the last calculation would more exactly be:

Price of apples = \$ 5.60

Quantity of apples = \$ 550 / \$5.60 = 98.2143

Real rate of interest = 98.2143 - 100 / 100 = - 1.7857 = minus 1.8 percent (not 2 percent)

The round off error is usually not a big problem at moderate rates of inflation; if it becomes so, note that the exact definition of the real rate of interest is:

Real rate of interest = nominal rate - inflation / ( 1 + inflation)

Be sure to treat the inflation rate as a decimal in the denominator of the above formula

. Note that this works for the calculation used as an illustration:

Real rate = 10 percent - 12 percent / (1 + 0.12) = - 2 percent / 1.12 = - 1.7857 percent.

Exercises:

Money lent/repaid          \$700                  \$735                  Money rate of interest =

Price of apples               \$ 10                   \$ 10.50              Inflation rate =

Quantity of apples                                                              Real rate of interest =

Price of apples               \$ 5                     \$ 5.50                Inflation rate =

Quantity of apples                                                              Real rate of interest =

Price of apples               \$ 7                     \$ 7.21                Inflation rate =

Quantity of apples                                                              Real rate of interest =

Price of apples               \$ 10                   \$ 15                   Inflation rate =

Quantity of apples                                                              Real rate =

Does the approximate formula for the real rate of interest work well for these examples?

Which one does it work best for?

Which one does it work worst for?