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In 1955, the last year when social security payments included only old-age payment (before disability) payments that year totaled $4.9 billion. For 2001, the figure was $433 billion (excluding Medicare, which was another $218 billion). During that period, the CPI rose at an average annual rate of 4.2%, and the number of people over 65 rose an average of 2.0% per year. What would social security have been in 2001 if the program had not expanded after 1955; i.e., if the only increases were due to inflation and population? Now suppose the CPI had been overstated by 1.1% per year. What would social security payments have been in 2001 if the actual rate of inflation had been used?

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The expert calculates the annual growth rate of social security payments.

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We need to calculate the annual growth rate if the only increases were due to inflation and population.
Each year, the inflation is 4.2% and population growth is 2%
Then the social security payment in the next period will be increased by:
(1+4.2%)(1+2%) - 1 = ...

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