Let's assume that savings banks give as much interest to depositors annually as the rate of inflation. The state deducts of the interest as tax. By what percentage does the real value of the state's interest tax revenue decrease if the inflation rate falls from to , and the real value of the deposit stock remains unchanged?
Solution
At the beginning of the first year, let the nominal value of the deposit be 100,000 units, and the real value be 100,000 "reals." At the end of the first year, the interest on the deposit is 25,000 units. Of this, 20,000 units belong to the deposit owners, and 5,000 units go to the state. In real value terms, the former is reals, and the latter is reals.
At the beginning of the second year, the deposit amount is still 100,000 reals, but its nominal value is now 125,000 units. (New savings cover the interest tax.) At the end of the second year, the interest on the deposit is units, of which 16,000 units belong to the deposit owners, and 4,000 units go to the state. The real value of the interest tax is reals. The state receives 1241 reals less compared to the previous year's 4000 reals. The decrease is approximately .