# Wealthy Maths: Nominal vs effective interest

In Latest, Wealthy Maths by Kristia van Heerden

A few years ago a local bank claimed to offer an exceptional interest rate on a cash savings product. A brief investigation by excited savers quickly revealed what they suspected: the claim sounded too good to be true because it was too good to be true. A difference between nominal interest and effective interest is at the heart of what rubbed potential savers the wrong way.

Interest rate basics

Interest is money paid for the privilege of using other people’s money. When we save, the bank pays us for the privilege of using our money. When we borrow, we pay the bank for the privilege of using its money. On the surface, the maths is pretty easy. Before you save or borrow money, the bank tells you how much interest you will receive (when you save) or pay (when you borrow).

For example, you decide to keep your emergency fund in a 30-day notice account with your bank. When you open the account, you are told you will receive 8% interest. If you put R20,000 in the account, you might assume you will receive:

20,000 x 8% = 1,600 every year

(Learn how to calculate percentages.)

However, you should ask whether the interest rate offered is a nominal or effective interest rate before you calculate how much you’ll have when you take out the money.

Nominal interest: what you see is what you get

You can think of nominal interest as the sticker price. When the bank says you will receive 8% nominal interest, it means you will receive the same amount of interest every time. If you left your R20,000 invested for five years and the bank calculates your interest once a year, you will receive R1,600 every year.

At the end of five years, you will have:

5 x 1600 = R8,000

When you withdraw your money, you will have R28,000. Your investment grew by 40%!

That’s pretty straight-forward. However, nominal interest rates don’t tell the full story.

Effective interest: what you see is only the beginning

As you already know, compounding is the reason why this saving and investing business actually makes us better off. Compounding is applied to interest, whether we pay it (when we borrow) or receive it (when we save). The effective interest rate takes compounding into account.

If you saved the same R20,000 that offered an interest rate of 8%, calculated and compounded once a year, things are looking even better for you!

In year one, your calculation would look the same as it did for your nominal interest rate:

20,000 x 8% = 1600

When the interest is paid into your account at the end of the first year, you would have:

20,000 + 1,600 = 21,600

This is where the fun really starts, because in year two you will earn 8% on your initial R20,000, as well as the R1,600 you earned in interest.

21,600 x 8% = 1,728. This is once again added to the money already in your account, which brings your total at the end of the second year to:

21,600 + 1,728 = 23,328.

If you keep going along this route (you can follow the formula we shared in this post), at the end of five years, you will have R29,386!

Remember, when you earned a nominal interest rate, you only got R28,000 at the end of five years. The additional R1,386 is interest you earned on interest. Your investment grew by 43%. That means you didn’t just earn 8% on your initial R20,000 investment. Your effective interest rate is 8.6%!

Why does it matter?

If your bank claimed you will earn 8.6% interest and you didn’t ask whether that would be nominal or effective interest, you could end up with less money than you anticipated. While the bank didn’t exactly lie when they said they offer an interest rate of 8.6%, they failed to mention the additional 0.6% is just 8% interest on your interest. It’s not wrong, but it’s not right either.

Unfortunately this also applies to the dark side of interest. When you borrow money, the bank will quote an interest rate amount. How often the interest is calculated and whether that quoted amount is a nominal or effective rate will have a huge impact on how much you end up paying in interest of the period. You can read more about the true cost of debt here.

Many of us avoid making financial decisions because we worry that we can’t do the maths. Luckily, there are only a few formulas you need to understand to make a good financial choices. This series of articles is dedicated to helping you understand how to do the calculations for yourself. Once you grasp these simple formulas, you can make better financial choices on the fly.

Wealthy Maths blog

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