Effective Annual Rate Calculator

More about the this EAR calculator so you can better use this solver: The effective annual rate ($EAR$) corresponds to the actual rate that is carried by a nominal annual rate ($r$). The difference between the nominal annual rate $r$ and the effective annual rate $EAR$ is due to the fact that for the $EAR$ there is a number of compounding periods.

How do you calculate effective annual rate?

For discrete compounding, the following formula is used:

$$EAR = \left( 1+\frac{r}{k}\right)^{ k} - 1$$

For continuous compounding, we get that $k \to \infty$, in which case we need to use the following formula instead.

$$EAR = e^{r} - 1$$

How to compute the effective annual rate excel?

For example, assume that the nominal rate is $r = 10\%$ and the compounding is done monthly, so the number of compounding periods is $k = 12$. The following formula needs to be used in Excel to get the effective annual rate: =FV(10%/12, 12, 0, -1)-1, which would yield a EAR of 10.47%.

How do you calculate the effective interest rate on a loan?

This is the same way you would calculate effective interest rate on a loan: You would take your nominal rate of $r$, and the number of compounding periods is $k = 12$, and you would use the Excel formula =FV(r/k, k, 0, -1)-1 . Or you could use our calculator, which will provide you will all the steps in the calculator.

Example of the calculation of the annual rate

Question: Find the effective rate of a nominal rate of 4%, compounded monthly.

Solution:

This is the information we have been provided with:

• The annual rate is $r = 0.04$, and the compounding is done monthly.

Therefore, the effective annual rate (EAR) is computed using the following formula:

$$\begin{array}{ccl} EAR & = & \displaystyle \left( 1+\frac{r}{k}\right)^{ k } - 1 \\\\ \\\\ & = & \displaystyle \left( 1+\frac{0.04}{12}\right)^{ 12 } - 1 \\\\ \\\\ & = & 0.0407 = 4.0742\%\end{array}$$ which means that the effective annual rate (EAR) for an annual rate of $r = 0.04$, with monthly compounding is $EAR =0.0407 = 4.0742\%$.

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