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Problem 3: Real Return (i.e., the Return after Inflation)

Paul just graduated from college and landed a “real” job that pays $23,000 per year.

a. What nominal rate will Paul need to earn in the future to maintain a 2 percent real return rate (assuming that inflation averages 1.96 percent per year)?

b. In nominal terms, what will Paul's salary be in ten years? Assume that his salary keeps up with inflation (assume inflation averages the same 1.96 percent per year).

c. In ten years, what will Paul's salary be in real terms? Assume he reaches his goal of maintaining a 2 percent real return.

a. To maintain a real return of 2 percent, Paul will need to make a nominal return of 4 percent in the future (assuming that inflation is 1.96 per year). To determine the nominal rate of return, remember the formula for real return: rr = ((1 + rn)/(1 + π)) – 1. Now plug in the values that you know: 1 + 0.02 = (1 + x %)/(1 + 0.0196). Solving for x results in a nominal return of 4 percent. Thus, Paul's nominal return must be 4 percent in the future to maintain a real return of 2 percent.

b. To maintain his current purchasing power ten years from now, Paul will have to make $28,036.87 in real terms.

This problem is very similar to those we have already discussed. Use the following values to solve this problem:

  • PV = –$23,000 (This is Paul's current salary)
  • I = 2 (Interest is replaced by inflation)
  • N = 10 (This is the number of years in the future)
  • FV = ?

The value of Paul's salary in ten years will be $28,036.87, assuming he achieves a real return of 2 percent.

c. His salary in real terms in 10 years will be $28,036.87.  This is calculated in the following way:

Real Return: -23,000 = PV, 2 = I (%), 10 = N, Solve for FV ? FV = $28,037


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