6.18313       The general formula for the effective annual rate is   APR n REFF a1 n b 1   where APR is the annual percentage rate and n is the number of compounding periods per year. Table 5A.1 presents the effective annual rates corresponding to an annual percentage rate of 6% per year for different compounding frequencies. As the compounding frequency increases, (1 APR/n)n gets closer and closer to eAPR, where e is the number 2.71828 (rounded off to the fifth decimal place). In our example, e.06 1.0618365. Therefore, if interest is continuously compounded, REFF .0618365, or 6.18365% per year. Using continuously compounded rates simplifies the algebraic relationship between real and nominal rates of return. To see how, let us compute the real rate of return first using an- nual compounding and then using continuous compounding. Assume the nominal interest rate is 6% per year compounded annually and the rate of inflation is 4% per year com- pounded annually. Using the relationship   Real rate 1 Nominalrate 1 Inflation rate r (1 R) R i (1 i) 1 1 i   we find that the effective annual real rate is   r 1.06/1.04 1 .01923 1.923% per year   With continuous compounding, the relationship becomes   er eR/ei eR i   Taking natural logarithms, we get   r R i   Real rate Nominal rate Inflation rate   all expressed as annual, continuously compounded percentage rates.