The US government offered a $100 bond for one year (it’s called a bill in this case, but for simplicity, we will call it a bond).
Interest = 5%
After a year, the investor is worth $105 (principal + interest).
If inflation = 5%, then the real return: Real interest rate = (1 + 5%)/(1 + 5%) – 1 = 0 The 5% above = interest, and the below = inflation rate.
So in this example, the investor’s purchasing power has not increased after a year because the year-end inflation rate = the nominal interest rate that was agreed upon at the beginning of the year.
But bonds insured against risk are as follows:
The same example, but the original and interest will be modified as follows: 1. After a year, the value of the asset will be increased by the rate of inflation. Inflation-adjusted principal = 100 x (1.05) = 105
2. Also after a year, the interest paid will be calculated based on the adjusted principal and not the face value of the bond at issue = $100, if: Inflation adjusted interest = 5% x 105 = 5.25
Please note that the interest rate has not changed (5%) but is 5% of a larger principal and thus became 5.25 instead of only $5.
So, after a year, the investor will receive:
Principal = 105 + Interest = 5.25 = 110.25 As if the nominal interest rate was 10.25%.
Now, the real interest can be calculated Real Interest Rate = (1+10.25%)/(1+5%) – 1 = 5%
The investor is fully insured against rising inflation and the nominal interest is equated to the real interest.