Jack invested $1200 into an account for 5-years with interest at j₂ = 6%.If the annual inflation rate is 2% for the first 2-years and 2.5% thereafter,what is the annual real rate of interest earned over the 5-years?

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Quizplus · Accepted Answer

The real rate of interest can be calculated using the formula: real rate = ((1 + nominal rate) / (1 + inflation rate)) - 1. For the first 2 years, the inflation rate is 2%, and for the next 3 years, it's 2.5%. The nominal rate is 6%. To find the average real rate over 5 years, we calculate the real rate for each period and then find the geometric mean.For the first 2 years with 2% inflation: real rate = ((1 + 0.06) / (1 + 0.02)) - 1 = 0.0392 or 3.92%For the next 3 years with 2.5% inflation: real rate = ((1 + 0.06) / (1 + 0.025)) - 1 = 0.0341 or 3.41%The average real rate over 5 years is the geometric mean of these rates: ((1.0392)^2 * (1.0341)^3)^(1/5) - 1 ≈ 0.0371 or 3.71%.

Jack Invested $1200 into an Account for 5-Years with Interest