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 \( EAR =0.0407 = 4.0742\%\).

Other financial calculators you may be interested in

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