**Nominal Interest Rate Formula (Table of Contents)**

## What is Nominal Interest Rate Formula?

The formula for the nominal interest rate can be calculated based on the effective annual rate of interest and the number of compounding periods per year. Mathematically, nominal interest rate formula is represented as below,

**Nominal interest rate = n * [(1 + i)**

^{1/n}– 1]where,

- i = Effective annual rate of interest
- n = Number of compounding periods per year

However, in the case of continuous compounding, the nominal interest rate equation is modified as below,

**Nominal interest rate = ln (1 + i)**

On the other hand, the nominal interest rate equation can also be calculated based on the real rate of interest and inflation rate. Mathematically, the nominal interest rate equation is represented as below,

**Nominal interest rate**

**= [(1 + Real interest rate) * (1 + Inflation rate)] – 1**

### Explanation

This formula can be calculated by using the following three steps:

**Step 1:** Firstly, figure out the effective annual rate of interest for the given investment based on the valuation of the investment at the beginning of the period and at the end of the period. The effective annual rate of interest is denoted by ‘i’ and is calculated as,

**i = (Value at the end of period/Value at the beginning of period – 1) * 100%**

**Step 2:** Next, figure out the number of compounding periods per year. The compounding can be quarterly, half-yearly, annually etc. The number of compounding periods of nominal interest rate per year is denoted by ‘n’. *(The step is not required for continuous compounding)*

**Step 3:** Finally, in the case of discrete compounding, it can be calculated using the following formula as,

**Nominal interest rate = n * [(1 + i) ^{1/n} – 1]**

On the other hand, in the case of continuous compounding, the nominal interest rate can be calculated using the following formula as,

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**Nominal interest rate = ln (1 + i)**

Again, the other equation for a nominal interest rate can also be determined by using the following three steps:

**Step 1:** Firstly, figure out the real rate of interest for the given investment.

**Step 2:** Next, figure out the inflation rate from various governmental information centers (e.g. Treasury Inflation-Protected Securities (TIPS) in the United States of America).

**Step 3:** Finally, it can be calculated based on the real rate of interest and the inflation rate as shown below,

**Nominal interest rate ****= [(1 + Real interest rate) * (1 + Inflation rate)] – 1**

**Example of Nominal Interest Rate Formula (with Excel Template)**

Let’s see some simple to advanced examples for the calculation of the Nominal Interest Rate Equation to understand it better.

#### Example #1

**Let us take an example where the nominal interest rate is to be calculated for one year with an effective rate of interest of 12%. The compounding is done:**

**Continuous****Daily****Monthly****Quarterly****Half Yearly****Annual**

Given, i = 12%

**#1 – Continuous Compounding**

Since continuous compounding,

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate calculation = ln (1 +12%)
- Nominal interest rate= 11.3329%

**#2 – Daily Compounding**

Since daily compounding, therefore n = 365

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate calculation = 365 * [(1 + 12% )
^{1/365}– 1] - Nominal interest rate= 11.3346%

**#3 – Monthly Compounding**

Since monthly compounding, therefore n = 12

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate calculation = 12 * [(1 + 12% )
^{1/12}– 1] - Nominal interest rate= 11.3866%

**#4- Quarterly Compounding**

Since quarterly compounding, therefore n = 4

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate calculation = 4 * [(1 + 12% )
^{1/4}– 1] - Nominal interest rate= 11.4949%

**#5 – Half Yearly Compounding**

Since half yearly compounding, therefore n = 2

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate = 2 * [(1 + 12% )
^{1/2}– 1] - Nominal interest rate= 11.6601%

**#6 -Annual Compounding**

Since annual compounding, therefore n = 1,

The nominal interest rate is calculated using the above formula as,

- Nominal interest rate calculation = 1 * [(1 + 12% )
^{1/1}– 1] - Nominal interest rate= 12.0000%

Therefore, the nominal interest rate for various compounding periods will be –

The below graph shows the nominal interest rate for various compounding periods

The above example shows that the equation for nominal interest rate depends not only on the effective rate of interest of the investment but also on how many times the rate compounding happens during a year and it increases with the increase in a number of compounding per year.

#### Example #2

**Let us take an example where the real interest rate on a one year fixed deposit is estimated to be 3% while the inflation rate during this period is expected to be 2%.**

Therefore, the nominal interest rate can be calculated using the other formula as,

Nominal interest rate = [(1 + 3%) * (1 + 2%)] – 1

So, the Nominal interest rate will be –

Nominal interest rate = 5.06%

### Relevance and Use

From an investor’s point of view, it is an indispensable part of investing as it is the interest rate stated on the face of a bond or loan. The nominal interest rate is the simplest form of interest rate and in the actual monetary price, it is the rate which a borrower pays to a lender to use his money. Further, the concept of nominal interest rate equation also captures the effects of compounding period per year which eventually helps in the calculation of redemption value at maturity.

On the other hand, the other form of the nominal interest rate can be used to determine the real rate of interest based on the inflation rate. The lower the inflation rate, the higher is the real rate of interest which is better as it supports the actual purchasing power in an economy.

### Recommended Articles

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