Effective Interest Rate (EIR) Calculator – Free Online Calculator

Definition of Effective Interest Rate

\[ \text{EIR or } i = \left(1 + \frac{r}{m}\right)^m – 1 \]

From the formula, 

Effective interest rate for t periods,

\[ \frac{i}{t} = (1 + i)^t – 1 \]
\[ \frac{i}{t} = \left(1 + \frac{r}{m}\right)^{mt} – 1 \]

Let’s consider a loan with a nominal interest rate of 5%, compounded quarterly. Using the effective interest rate formula:

\[ \text{EIR} = \left(1 + \frac{0.05}{4}\right)^4 – 1 \]
\[ \text{EIR} \approx \left(1 + 0.0125\right)^4 – 1 \]
\[ \text{EIR} \approx \left(1.0125\right)^4 – 1 \]
\[ \text{EIR} \approx 1.050945 – 1 \]
\[ \text{EIR} \approx 0.050945 \]

So, the effective interest rate for this loan is approximately 5.09%. This reflects the actual annual cost of borrowing when considering compounding and provides a more accurate measure compared to the nominal interest rate.

If the compound frequency is incessant, you need to apply:

EIR = e^m – 1 [where e stands for constant of exponent.]

To have a clear idea, you have to understand the nominal interest rate.

Nominal Interest Rate

The formula for calculating the Nominal Interest Rate (r) is straightforward. The formula is:

\[ r = \frac{\text{Nominal Interest Paid}}{\text{Principal Amount}} \times 100 \]

For example, if you pay $800 in nominal interest on a $10,000 loan, the nominal interest rate would be:

\[ r = \frac{800}{10000} \times 100 = 8\% \]

Therefore, the nominal rate in this example is 8%. For a more accurate measure of the overall cost or return, it’s essential to consider the Effective Interest Rate (EIR) when compounding is involved.Comparison between effective interest rate (EIR) and nominal interest rate is as follows:

Though not handy, you can also make an effective interest rate calculator excel by using the following formula in cell C2.

Or in C4.