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Interest rates can be a bit tricky to understand, especially when compounded. A **nominal rate** is the rate that banks or financial institutions advertise, without taking compounding into account. Think of it as the headline interest rate you see in marketing materials.
However, what does 'compounded' mean in this context? Well, compounding reflects how often the interest gets calculated and added to the account, which in turn increases the amount of interest that gets calculated next time.
For instance, if you have a nominal rate of 6.5% compounded quarterly, it means the rate is divided over four quarters of the year. This affects the actual interest accrued, often making it more beneficial than the nominal rate suggests.

• The more frequent the compounding, the higher the effective rate grows.
• Nominal rates don't give the full picture when compounding is involved.

When a bank states that its interest is compounded quarterly, it means the interest calculation and application occur four times a year. This method splits the annual interest rate into four equal parts.
For example, if you have a 6.5% nominal rate compounded quarterly, each quarter will calculate interest at a rate of 1.625% (which is 6.5% divided by 4).
Each time the interest is compounded, the new balance has the previously added interest included, leading to **interest on interest**. This effect can considerably impact savings over time.

• Quarterly compounding means interest is calculated every three months.
• Over a year, this method increases the actual interest earned beyond the nominal rate.

Daily compounding, as the name suggests, calculates and adds interest to the balance once every day. This type of compounding effectively divides the nominal interest rate by 365 days in the year.
Even though each daily amount might seem small, the cumulative effect is quite significant because the interest keeps applying to the "fresh" balance each day.
For a nominal rate of 6.6% compounded daily, each day's interest would be calculated at approximately 0.01808% (which is 6.6% divided by 365). Over time, this means you're getting interest not just on your initial deposit, but on the interest generated each day too.

• More frequent compounding generally means a higher effective interest rate.
• Daily compounding captures every day's potential for growth.

The Effective Annual Rate (EAR), commonly known as effective yield, represents what you actually earn over a year after compounding. It's a more accurate representation of earned interest compared to the nominal rate.
To calculate EAR, you use the formula: \[(1 + \frac{r_{nom}}{n})^n - 1\] Where:

• \(r_{nom}\) is the nominal interest rate,
• \(n\) is the number of compounding periods in a year.

Applying this to our example:

• For 6.5% quarterly compounded, the EAR is approximately 6.653%.
• For 6.6% daily compounded, it's about 6.817%.

The second rate is more favorable because daily compounding better captures the essence of compound growth by applying it more frequently. Choosing the account with the higher EAR is typically the better investment choice.