  # Comparing Effective Interest Rate vs Nominal Interest Rate

An effective interest rate is a return you get from investing. In contrast, a nominal interest rate is a stated payoff offered by an investment. An experienced investor may sometimes ignore the petty differences between the terms.

However, the effect caused by the possible figures behind the decimal in a percentage can be enormous and significant. Before you decide to invest and see the familiar names, you may make a wise investment decision by recalling the following.

## How to Compare Nominal and Effective Interest Rates

You can invest smartly next time by reminding the differences between effective and nominal rates.

 Effective interest rate Nominal interest rate *General formula (1 + r1/p)^p – 1 (1 + r2)^(1/p) – 1 Compounding Yes No Compounding frequency Annual, quarterly, monthly and daily or unlimited No Return Increased returns due to rolling return on interest, besides principal A whole-of-period return only Which is higher? Higher if compounded more than one period, the same return if compounded annually Lower

*r1 is the nominal interest rate, while r2 is the effective interest rate. P is compounding periods.

An effective interest rate is a compounding rate with interest rolling on interests, while a nominal interest rate is an interest rate of a single period. Also, the compounding frequencies can be unlimited for effective rates, yet, only one nominal rate exists. These two rates are equivalent if an effective rate is compounded annually.

## More Details on Effective Interest Rate

An effective interest rate in investing is an accumulated return rolling over more than a period. In other words, it is a total return measured by a principal and interests accrued and reinvested from the previous periods. An effective interest rate is a whole-value measurement of return.

### How it Works

An example lets you see it more clearly. Joan puts \$1,000 into a bank account, earning an effective interest rate of 0.5% half-yearly. Before depositing the money, Joan wants to know the effective annual interest rate offered by the bank; suppose she wants to make a 1-year investment.

The sum of \$1,000 in the bank account returns \$5(1000 x 0.5%) as stated after 6 months, and the total amount is \$1,005. Joan intends to stay the same for another half-year without withdrawing the principal and interests.

By year-end, the interest earned is \$5.03. The total amount in Joan’s account is 1010.03(\$1005 + \$5.03.) The story does not end here. The annual effective interest rate is 1.003%(\$1,010.03/1000.) for 1 year’s effective interest rate from Joan’s deposit.

### Formula

You can calculate an effective interest rate based on a general formula: (1 + r/p)^p – 1.

Whereas r is the interest rate stated, m is the number of periods.

A clear example of the above formula is:

A nominal interest rate(to be discussed later) is 2%, compounded quarterly; what’s the effective annual effective interest rate?

Answer: (1 + 2%/4)^4 – 1= 2.02%

The term “compound” means money is rolled over and accumulated for periods without any withdrawals.

An effective annual interest rate is 0.02% more than a nominal interest rate of 2%. The effective annual interest rate of 2.02%, if compounded quarterly, is the actual rate of return an investor gets after 1 year.

## More Details on Nominal Interest Rate

Contrary to an effective interest rate, a nominal interest rate is a stated interest rate of return. The rate of return is also the total interest earned over specific periods, excluding the compounding effect. Most banks offer deposit rates by nominal interest rates paid half-yearly.

### How It Works

Referring to the bank deposit example above, Joan wants to know her deposit’s nominal annual interest rate.

Calculating a nominal effective interest rate is more straightforward than an effective one. In Joan’s case, we combine 2 half-yearly interest rates and reach the nominal rate: 0.5% x 2 = 1%. Usually, a bank or a bond issuer states to clients or investors a nominal interest rate like a one-year deposit rate or a half-year coupon rate.

### Formula

If you plan to dig out the return in detail, a calculation is here to help. By looking for a nominal annual interest rate, Joan needs to have 2 things on hand: the number of compounding periods and a stated rate for a period.

Joan can use the general formula: r x p, where the rate is 0.5% per period, and the number of periods is 2. The nominal annual interest rate is 0.5% x 2 = 1% but compounded half-yearly. The advanced formula is available: (1 + r/p)^p – 1.

Joan should know a nominal interest rate is no more than an effective one. Therefore, the total return she earns at the end of the period is measured by an effective interest rate. ## What is the Relationship between an Effective Interest Rate and a Nominal Interest Rate?

Both nominal and effective rates are constant pop-ups in the investment literature. Understanding their interchangeability when you invest helps you clarify their relationship and expand your chance for investing success.

### An example

Financial institutions offer products with various rates of return, you are responsible for determining how much you can earn.

### Calculation

For example, You want to know a bank deposit with a nominal interest rate, like a 1-year deposit with a yearly rate of 2%, compounded monthly. To determine an effective annual interest rate, you need a formula: (1 + r/p)^p – 1, as stated previously.

#### The Process

(1 + 2%/12)^12 – 1= 2.02%. The effective annual interest rate for a 1-year deposit is 2.02%, with a nominal interest rate of 2%. Therefore, the bank pays you an interest of \$202 if you deposited \$10,000 a year before. Hence, the effective interest rate is a genuine return instead of a nominal one.

Conversely, you already know the effective annual interest rate and want to know the nominal interest rate to compare and discover the best bank rate.

Using the example above, you calculate by the formula: (1 + r)^(1/p) – 1. In this case, the nominal interest rate is 2% = (1 + 2.02%)^(1/12).

### To sum up

Effective interest rate: (1 + r1/p)^p – 1, where r1 is a state or nominal interest rate.

Nominal interest rate: (1 + r2)^(1/p) – 1, where r2 is an effective interest rate.

Both rates are essential to investors in making rate decisions. You use the effective interest rate when calculating the real profits on investment. Yet you can use the nominal interest rates to compare product rate differences.

## What is a Compounding Period?

A compounding period is a timespan when a return increases due to the accrued interest from the previous period besides the principal.

Instead of a single period, the more compounding periods, the higher the return.

In other words, an interest rate compounded quarterly accumulates more than half-yearly. And an interest rate compounded monthly produces more returns than quarterly.

Likewise, if you borrow money on a compounded basis from a bank, in that case, you have to pay more loan interest using an effective interest rate as the bank demands compounded interest payments, which are more than single interest.

## What is a Real Rate of Return?

A real rate of return is a net investment gain expressed in a percentage after deducting the inflation factor. For example, if a bond yields a 5% gain after a year and the inflation rate is 2%, the real rate return is 3% = 5% – 2%. For calculation purposes, the formula is “real rate of return = nominal rate of return – inflation rate.”

Investment professionals think a real return should be available only in exchange for inflation loss. Another factor to be considered is interest expense if you borrow to invest by taking advantage of low leverage costs.

## Which is A Better Measure: Effective Interest Rate, Nominal Interest Rate, or Real Rate of Return?

It depends on investment criteria and legal requirements. Every jurisdiction has different rules and regulations concerning the use of interest rates adopted on investment products.

Besides, nominal interest rates are fit for comparison purposes due to their single format, while quoted effective interest rates are difficult to understand. Investors should determine actual returns based on effective interest rates as they are accurate. Finally, investors may need a real return from an economic view by deducting the inflation factor.

## Bottom Up

An effective interest rate measures the compounding effect of accrued interests from the previous period and is fit for determining an investment result. A nominal interest rate is a whole-of-period calculation suitable for demonstration and comparison. A real rate of return is a rate net of inflation.

Key Takeaways

• An effective interest rate is a measure based on the compounding growth of accrued interest from the previous period.
• An nominal interest rate is calculated based on a single period.
• The more compounded periods are, the higher the effective interest rate.
• An effective interest rate is higher than a nominal interest rate except for a single period.

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