The effective annual rate on an account that pays 5% interest, compounded quarterly, is greater than the effective annual rate on an account that pays 4.8% interest, compounded continuously.

Question

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The effective annual rate (EAR) for an account that pays 5% interest, compounded quarterly, is calculated using the formula $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate and $n$ is the number of compounding periods per year. For 5% interest compounded quarterly, this gives $EAR = (1 + \frac{0.05}{4})^4 - 1 = 1.050945\% $. For an account with 4.8% interest compounded continuously, the EAR is calculated using $EAR = e^r - 1$, where $e$ is the base of the natural logarithm, approximately equal to 2.71828, and $r$ is the annual interest rate. This gives $EAR = e^{0.048} - 1 = 4.911123\%$. Comparing these, the EAR for the 5% compounded quarterly is indeed greater than the 4.8% compounded continuously.

The Effective Annual Rate on an Account That Pays 5