# StevenClark.com.au

## Time Value of Money: Nominal versus Effective Interest Rates

In Time Value of Money: Present & Future and Time Value of Money: Financial Tables we discussed fixed amounts and moved onto Time Value of Money: Ordinary Annuities, Time Value of Money: Annuities Due and Time Value of Money: Mixed Streams. Then we discussed Time Value of Money: Compound Interest (redux). At this point it’s important to understand nominal versus effective annual rates of interest.

### Nominal & Effective Rates of Interest

It is important to be able to differentiate between the interest that you sign up for in a contract and the amount of interest that actually accrues in the account.

The Nominal Interest Rate (NIR) is the interest rate stated in the contract. While, the Effective Interest Rate (EIR) is the rate of interest that is paid or accrues and this takes into account the effect of interest compounding over time. If compounding of interest is annual then the NIR and the EIR will be the same.

### Calculating the Effective Interest Rate

The formula to calculate the EAR, where i represents the NIR and m represents the compounding frequency:

EAR = (1 + (i / m))m – 1

For a NIR of 12 per cent we can look at the calculations for annual and quarterly EIR:

• Effective Interest Rate = (1 + (0.12 / 1))1 – 1
• Effective Interest Rate = 1.12 – 1
• Effective Interest Rate = 0.12

This demonstrates that the EIR of 12 per cent does equal the NIR of 12 per cent when compounding annually. However, this is not the case for quarterly compounding (or any compounding shorter than a year):

• Effective Interest Rate = (1 + (0.12 / 4))4 – 1
• Effective Interest Rate = (1.03)4 – 1
• Effective Interest Rate = 1.1255 – 1
• Effective Interest Rate = 0.1255

Quarterly compounding produces an EIR of 12.55 per cent from a NIR of 12 per cent. The shorter the compounding period the larger the EIR becomes.

### The Next Step: More Applications of Time Value of Money

The difference between NIR and EIR is one of those small but fundamental pieces of knowledge that you need to make effective financial decisions. In the next article we will look at other applications of the Time Value of Money.

I would also advise you to pick up any decent copy of a managerial finance textbook to underpin these articles and to complete the exercises that will cement this understanding at the end of each chapter. The textbook will also provide more precise context important to your understanding.

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My name is Steven Clark and I live in the Derwent Valley in Southern Tasmania. I have an MBA (Specialisation) and a Bachelor of Computing from the University of Tasmania. I'm a mazer & a yeast farmer (making beer, fruit wine and mead as by-products of continuous improvement in my farming practices). I'm a photographer, although my film cameras are currently silent. I do not tolerate idiots. I do not tolerate bigotry. I do not tolerate excuses. Let's be clear, if you sit with my enemies you my are my enemy for life.

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