# Finance

## Real Interest Rate - Formula and Examples

For purposes of the following explanation we will adopt the viewpoint of the lenders (the strong party).

Real interest is the term used to calculate the increase in purchasing power that the loan has given us after the borrower has paid his debt: Interest and principal.

We granted Bill a \$1,000 one-year loan at the beginning of the year (date A) at 12% nominal interest. At the end of the year, we will receive \$1,120 from Bill (\$1,000 for the principal + \$120 in interest). We will examine the added purchasing power that we have obtained under three scenarios concerning changes in the Consumer Price Index during the period:

Scenario 1 - the Consumer Price Index remains constant (0% inflation).

Scenario 2 - the Consumer Price Index rises 5%.

Scenario 3 - the Consumer Price Index rises 20%.

The calculation will be accompanied by an example relating to the anemones, which cost \$1 each on date A. The price of anemones on date B changes, in accordance with the change in the Consumer Price Index.

Table 1.5

 Scenario 1 Scenario 2 Scenario 3 0% inflation 5% inflation 20% inflation Situation on date A: Value of the principal \$1,000 \$1,000 \$1,000 Price of anemones \$1 \$1 \$1 Number of anemones we could have bought 1,000 anemones 1,000 anemones 1,000 anemones Situation on date B: Value of principal + interest \$1,120 \$1,120 \$1,120 Price of the anemones \$1 \$1.05 \$1.20 Number of anemones we could have bought 1,120 anemones 1,067 anemones 933 anemones Change in the number of anemones between date A and date B. 120 67 67 less Additional (or fewer) anemones (real increase or decrease in purchasing power) 12% 6.7% -6.7% Comment Our situation is 12% better. Our situation is better, but only by 6.7%. Our situation has worsened by 6.7%.

On date A, we have the opportunity to buy 1,000 anemones with the sum we lent to Bill (\$1,000). Within the framework of the following table, we calculate how many anemones we can buy on date B under each of the three scenarios.

Real Interest Rate - Formula and Examples581