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IAI Actuarial Core Principles · Business Economics · Recent macroeconomic history

Consumer prices in an economy rose from an index of 125.0 to 133.75 over one year. A bank pays a nominal deposit rate of 5% for that year. Using the approximate relationship (nominal rate minus inflation), what was the approximate real return, and what does it imply for savers?

Inflation was 7% as the index rose from 125 to 133.75. With a 5% nominal deposit rate, the approximate real return is minus 2%, meaning savers lost purchasing power despite earning interest.

  1. A-2.0%, so savers lost purchasing powerCorrect
  2. B+5.0%, so savers kept all purchasing power
  3. C+2.0%, so savers gained purchasing power
  4. D-7.0%, so savers lost more than the inflation rate
  5. 0.0%, so savers broke even exactly

Explanation

Inflation = (133.75 - 125)/125 = 8.75/125 = 7%. Approximate real return = 5% - 7% = -2%. Savers therefore lost purchasing power. Adding the rates instead gives the wrong +12%, and ignoring inflation gives +5%.

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