Financial Modeling Tutorials

- Financial Modeling Basics
- Excel Modeling
- Financial Functions in Excel
- Sensitivity Analysis in Excel
- Sensitivity Analysis
- Capital Budgeting Techniques
- Time Value of Money
- Future Value Formula
- Present Value Factor
- Perpetuity Formula
- Present Value vs Future Value
- Annuity vs Pension
- Present Value of an Annuity
- Doubling Time Formula
- Annuity Formula
- Annuity vs Perpetuity
- Annuity vs Lump Sum
- Deferred Annuity Formula
- Internal Rate of Return (IRR)
- IRR Examples (Internal Rate of Return)
- NPV vs XNPV
- NPV vs IRR
- NPV Formula
- NPV Profile
- NPV Examples
- PV vs NPV
- IRR vs ROI
- Break Even Point
- Payback Period & Discounted Payback Period
- Payback period Formula
- Discounted Payback Period Formula
- Profitability Index
- Cash Burn Rate
- Simple Interest
- Simple Interest vs Compound Interest
- Simple Interest Formula
- CAGR Formula (Compounded Annual Growth Rate)
- Effective Interest Rate
- Loan Amortization Schedule
- Mortgage Formula
- Loan Principal Amount
- Interest Rate Formula
- Rate of Return Formula
- Effective Annual Rate
- Effective Annual Rate Formula (EAR)
- Daily Compound Interest
- Monthly Compound Interest Formula
- Discount Rate vs Interest Rate
- Rule of 72
- Geometric Mean Return
- Real Rate of Return Formula
- Continuous compounding Formula
- Weighted average Formula
- Average Formula
- Average Rate of Return Formula
- Mean Formula
- Mean Examples
- Population Mean Formula
- Weighted Mean Formula
- Harmonic Mean Formula
- Median Formula in Statistics
- Range Formula
- Outlier Formula
- Decile Formula
- Midrange Formula
- Quartile Deviation
- Expected Value Formula
- Exponential Growth Formula
- Margin of Error Formula
- Decrease Percentage Formula
- Percent Error Formula
- Holding Period Return Formula
- Cost Benefit Analysis
- Cost Benefit Analysis Examples
- Cost Volume Profit Analysis
- Opportunity Cost Formula
- Opportunity Cost Examples
- Mortgage APR vs Interest Rate
- Normal Distribution Formula
- Standard Normal Distribution Formula
- Normalization Formula
- Bell Curve
- T Distribution Formula
- Regression Formula
- Regression Analysis Formula
- Multiple Regression Formula
- Correlation Coefficient Formula
- Correlation Formula
- Population Variance Formula
- Covariance Formula
- Coefficient of Variation Formula
- Sample Standard Deviation Formula
- Relative Standard Deviation Formula
- Standard Deviation Formula
- Volatility Formula
- Binomial Distribution Formula
- Quartile Formula
- P Value Formula
- Skewness Formula
- R Squared Formula
- Adjusted R Squared
- Regression vs ANOVA
- Z Test Formula
- F-Test Formula
- Quantitative Research

Related Courses

**Effective Interest Rate or Annual Equivalent Rate –**Knowing how Effective Interest Rate works is one of the most important lessons for first-time investors.

If you’re just starting out or have never heard about annual equivalent rate (AER), you’re at the right place.

In this article, we will talk about the Effective Interest Rate in detail.

Let’s get started.

## What is Effective Interest Rate or Annual Equivalent Rate(AER)?

When an investor invests into an instrument, she earns an interest.

However, there’s a twist in the equation.

The investor doesn’t exactly earn what is written as an interest rate on the instrument.

Rather she earns an effective interest rate which is called annual equivalent rate.

But how we would calculate the annual equivalent rate (AER)?

First, let’s look at the AER formula. And then we will see the interpretation and practical examples.

## Effective Interest Rate Formula

The Effective Interest Rate formula is very simple.

Annual Equivalent Rate or Effective Interest Rate Formula = (1 + i/n) ^{n }– 1

Here, i = the annual interest rate that has been mentioned in the instrument.

n = It represents the number of compounding periods per year.

**Recommended Courses**

## Annual Equivalent Rate Interpretations

Compounding changes the interest rate.

That’s why the interest rate written on the instrument isn’t effective interest rate for the investor.

For example, if 11% interest rate is written on the instrument and the interest rate gets compounded four times a year, then the effective interest rate can’t be 11%.

4.9 (927 ratings)

What would it be then?

It would be – (1 + i/n)^{ n }– 1 = (1 + 0.11/4) ^{4 }– 1 = 1.1123 – 1 = 0.1123 = 11.23%.

That means 11.23% would be the effective interest rate for the investor.

Even if the change is meager, it’s not the same as the annual interest rate mentioned in the instrument.

Now, we will look at a few practical examples. In these examples, we will go deep and understand the nitty-gritty of Effective Interest Rate.

## Annual Equivalent Rate Example

In this section, we will take three examples and will see how Effective Interest Rate works.

The first two examples would be simple examples.

In the third example, we will go deep.

#### Effective Interest Rate Example#1

**Ting bought a particular instrument. The interest rate mentioned on the instrument is 16%. He has invested around $100,000. The instrument compounds annually. What would be the effective interest rate (AER) for this particular instrument? How much he would get every year as an interest?**

This example has a twist.

This example illustrates why the mentioned annual interest rate and the effective interest rate isn’t same.

The effective interest rate and the annual interest rate aren’t always same because the interest gets compounded a number of times every year. Sometimes, the interest rate gets compounded semi-annually, quarterly, or monthly. And that’s how the effective interest rate (AER) differs from the annual interest rate.

This example shows you that.

Let’s calculate.

Since the interest rate gets compounded yearly, here’s would be the effective interest rate formula –

(1 + i/n)^{ n }– 1 = (1 + 0.16/1)^{ 1 }– 1 = 1.16 – 1 = 0.16 = 16%.

That means in this particular example, there would be no difference between the annual interest rate and annual equivalent rate (AER).

Every year Ting would get the interest of = ($100,000 * 16%) = $16,000 on the instrument.

#### Annual Equivalent Rate Example#2

**Tong bought a particular instrument. The interest rate mentioned on the instrument is 16%. He has invested around $100,000. The instrument compounds six times a year. What would be the annual equivalent rate (AER) for this particular instrument? How much he would get every year as an interest?**

This is just an extension of the previous example.

But there’s a huge difference.

In the previous example, the instrument got compounded once a year which made the annual interest rate similar to the annual equivalent rate.

However, in this case, the scenario is completely different.

Here we have the interest rate that gets compounded six times a year.

So, here’s the formula of the annual interest rate –

(1 + i/n)^{ n }– 1 = (1 + 0.16/6)^{ 6 }– 1 = 1.171 – 1 = 0.171 = 17.1%.

You can now see that if the interest rate gets compounded six times a year, the annual equivalent rate becomes quite different.

Now, as we have an effective interest rate, we can calculate the interest Tong will get at the end of the year.

Tong will get = ($100,000 * 17.1%) = $17,100.

If we compare the interest Ting gets in the previous example with the Tong gets as the interest rates compound differently, we will see that there’s around $1100 of difference in interest.

#### Annual Equivalent Rate Example#3

**Ping has invested in an instrument. She has invested $10,000. The interest rate mentioned in the instrument is 18%. The interest gets compounded monthly. Find out how in the first year Ping will receive interest every month.**

This is a much detailed example of the annual equivalent rate.

In this example, we will show how the calculation actually happens without using the Effective Interest Rate formula.

Let’s have a look.

Since the interest rate gets compounded monthly, the actual break-up of mentioned interest rate per month is = (18/12) = 1.5%.

- In the first month, Ping will receive an interest of = (10,000 * 1.5%) = $150.
- In the second month, Ping will receive an interest of = {(10,000 + 150) * 1.5%} = (10,150 * 1.5%) = $152.25.
- In the third month, Ping will receive an interest of = {(10,000 + 150 + 152.25) * 1.5%} = (10,302.25 * 1.5%) = $154.53.
- In the fourth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53) * 1.5%} = (10,456.78 * 1.5%) = $156.85.
- In the fifth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85) * 1.5%} = (10,613.63 * 1.5%) = $159.20.
- In the sixth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20) * 1.5%} = (10,772.83 * 1.5%) = $161.59.
- In the seventh month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59) * 1.5%} = (10,934.42 * 1.5%) = $164.02.
- In the eighth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02) * 1.5%} = (11098.44 * 1.5%) = $166.48.
- In the ninth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02 + 166.48) * 1.5%} = (11264.92 * 1.5%) = $168.97.
- In the tenth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02 + 166.48 + 168.97) * 1.5%} = (11433.89 * 1.5%) = $171.51.
- In the eleventh month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02 + 166.48 + 168.97 + 171.51) * 1.5%} = (11605.40 * 1.5%) = $174.09.
- In the twelfth month, Ping will receive an interest of = {(10,000 + 150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02 + 166.48 + 168.97 + 171.51 + 174.09) * 1.5%} = (11779.49 * 1.5%) = $176.69.

The total interest Ping got for the year is –

- (150 + 152.25 + 154.53 + 156.85 + 159.20 + 161.59 + 164.02 + 166.48 + 168.97 + 171.51 + 174.09 + 176.69) = $1956.18.

Now, if we use the effective interest rate formula and calculate, we will see –

- Effective Interest Rate formula = (1 + i/n)
^{ n }– 1 = (1 + 0.18/12)^{12 }– 1 = 1.195618 – 1 = 0.195618 = 19.5618%.

So, the interest Ping would receive = ($10,000 ^ 19.5618%) = $1956.18.

## Annual Equivalent Rate – Effective Interest Rate in Excel

For finding the Effective Interest Rate or Annual Equivalent Rate in excel, we use the excel Function EFFECT.

- nominal_rate is the interest rate
- npery is the number of compounding periods per year

Let us see the example below

- If you have a nominal interest rate of 10% compounded annually, then the Effective Interest Rate or Annual Equivalent Rate is same as 10%.
- If you have a nominal interest rate of 10% compounded six monthly, then the Annual Equivalent rate is same as 10.25%.
- If you have a nominal interest rate of 10% compounded quarterly, then the Annual Equivalent rate is same as 10.38%.
- If you have a nominal interest rate of 10% compounded monthly, then the Annual Equivalent rate is same as 10.47%.
- If you have a nominal interest rate of 10% compounded daily, then the effective interest rate is same as 10.52%.

### Effective Interest Rate Video

## Suggested Readings

This was the guide to Effective Interest Rate or Annual Equivalent Rate – Effective Interest Rate Formula and AER Examples. For further learnings, you may refer to the following articles

- Nominal Interest Rate | Disadvantages | Example
- Simple Interest Rate Formula
- Nominal Interest Rate Formula
- Top 15 Financial Functions in Excel
- NPV vs IRR differences
- NPV vs XNPV | Top Differences
- Time Value of Money

- 35+ Courses
- 120+ Hours of Videos
- Full Lifetime Access
- Certificate of Completion

- Basic Microsoft Excel Training
- MS Excel 2010 Training Course: Advanced
- Microsoft Excel Basic Training
- Microsoft Excel 2013 – Advanced
- Microsoft Excel 2016 – Beginners
- Microsoft Excel 2016 – Advanced