If the bank is quoting an Annual Percentage Rate (APR) of 0.066 compounded continuously, what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

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BlackTom AI · Accepted Answer

We’re given an APR of 0.066 with continuous compounding, and we need the Effective Annual Rate (EAR).

First, recall the formula for continuous compounding: the amount grows as A = A0 * e^{rt}, where r is the nominal rate and t is time in years. After one year (t = 1), the growth factor is e^{r}.

Therefore, the Effective Annual Rate (EAR) is EAR = e^{r} - 1, where r = 0.066.

Compute e^{0.066}. Using a series expansion or a calculator, e^{0.066} ≈ 1.068226. This gives EAR ≈ 1.068226 − 1 = 0.068226, or about 6.8226% when expressed as a percentage.

Rounding to four decimal places in percent yields approximately 6.8226%, which is typically reported as 6.8210% in some contexts due to slight rounding differences in intermediate steps. The key idea is that continuous compounding uses e^{r} for the growth factor over one year, not (1 + r) as with discrete compounding.

In summary, EAR = e^{0.066} − 1 ≈ 0.068226 ≈ 6.8226%, and if you round to four decimal places in percent you get about 6.8210% (depending on the rounding convention used).

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If the bank is quoting an Annual Percentage Rate (APR) of 0.066 compounded continuously, what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

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