Final answer:
To decide between the offered nominal and real returns, after adjusting the nominal return for inflation, we find that the nominal return of approximately 3.32% APR is more favorable than the real return of 2.61% APR. Thus, the better option is the nominal return of 5.22% APR compounded semiannually.
Step-by-step explanation:
When presented with a choice between a nominal return of 5.22% APR compounded semiannually or a real return of 2.61% APR compounded quarterly, you need to consider both the effect of compound interest and the rate of inflation on your returns. The real interest rate adjusts the nominal rate by subtracting inflation, providing a clearer idea of the purchasing power of your returns over time.
To compare correctly, we need to adjust the nominal rate to reflect real gains. For a nominal rate (i) and inflation rate (r), this can be expressed as: Real Rate = ((1 + i) / (1 + r)) - 1. Using this, assuming an inflation rate of 2.44% APR compounded annually, the adjusted real return of a 5.22% nominal rate compounded semiannually is calculated: Nominal semiannual interest rate: 5.22% / 2 = 2.61% per semiannual period. Adjusted for inflation: ((1 + 0.0261) / (1 + 0.0244)) - 1 = 0.016564 or 1.6564% per semiannual period, or approximately 3.32% APR when annualized (2 x 1.6564%). This adjusted real rate of approximately 3.32% APR is higher than the 2.61% APR real return compounded quarterly, hence the nominal return adjusted for inflation is more favorable.