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When it comes to growing your savings, compounded interest is the silent workhorse that can make a big difference over time. Simply put, compounded interest is interest calculated on the initial principal, which also includes all the accumulated interest from previous periods. This is a step up from simple interest, where you only earn interest on the principal amount.

Here's where it gets interesting – with each compounding period, you earn interest not just on your original amount, but also on the interest that has been added to it previously. It’s as if your interest is earning its own interest, creating a snowball effect. The more frequently the interest is compounded, the more you will earn. This is precisely why the frequency of compounding impacts the Effective Annual Interest Rate (EAR) and your overall return on investment.

The nominal interest rate is the percentage increase in money you can expect to earn or pay in one year before considering compounding. It's like the advertised rate you see on a bank’s brochure. However, this number can be deceiving because it doesn't take into account the effects of compounding. To illustrate, a nominal interest rate of 5% might sound great, but if this rate is compounded monthly, the money you earn could be significantly more due to the compound interest.

The nominal interest rate is essentially the 'simple' interest rate. For instance, if you deposit \(1000 in a savings account with a 4% nominal interest rate compounded annually, you'll have \)1040 at the end of the first year. To compare different interest offers accurately, especially when they compound at different intervals like weekly or daily, we convert the nominal rate into the Effective Annual Interest Rate (EAR).

The term compounding periods refers to how often the interest is applied to your balance. Common compounding frequencies include daily, monthly, quarterly, semi-annually, and annually. Obviously, the more frequent the compounding periods, the more times your money will be subject to interest calculations, and the faster it will grow due to compounded interest.

Let's consider an example to make sense of this concept. If a bank offers a nominal interest rate with annual compounding, the interest is calculated and added to your principal once a year. But with monthly compounding, this process happens twelve times a year at smaller intervals. This results in a higher Effective Annual Interest Rate because the interest has more opportunities to be calculated and added to the principal, leading to more substantial growth over the same period. Hence, when evaluating investment options, understanding the compounding periods is vital in determining the true rate of return on your savings or investment.