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Annual compounding refers to the process of calculating interest once a year on a deposit or loan. It’s one of the simplest forms of interest compounding.
When you have a savings account or an investment in a bank that compounds interest annually, the interest you've earned is added to your principal once every year. This means that the following year, you will earn interest on the new total amount, which includes the added interest from the previous year.

Some important characteristics of annual compounding include:

• Interest is computed only once throughout the year.
• The formula used is simple: \[EAR = (1 + r/n)^n - 1\]When compounded annually, \(n = 1\), and the formula simplifies to \[EAR = (1 + r)^1 - 1\]

In the context of Bank A, with a nominal interest rate of 4%, the Effective Annual Rate (EAR) is also 4%. Thus, when considering a full year, the interest you earn remains straightforward to calculate and understand.

Daily compounding refers to interest being calculated and added to the balance every day. This means that every day, your principal amount becomes slightly larger, and you earn interest on this increased amount the next day.
Due to being calculated more frequently than annual compounding, daily compounding can lead to a larger overall increase in your investment or saved money by the end of the year.

Key features of daily compounding include:

• Interest is calculated 365 times a year, hence \(n = 365\).
• The formula looks like: \[EAR = (1 + r/365)^{365} - 1\]
• This can result in a slightly higher EAR than the nominal rate since interest is continuously being added and recalculated.

In our exercise, Bank B offers a 3.5% nominal interest rate but due to daily compounding, the EAR comes out to approximately 3.5617%. Thus, over a year, more frequent compounding can marginally enhance returns.

When comparing interest rates, particularly for deciding between two banks, the Effective Annual Rate (EAR) becomes crucial. This rate reflects the real return on your investment, considering the effects of compounding.

Comparing the EAR involves several considerations:

• Bank A has an EAR of 4% from annual compounding, whereas Bank B offers an EAR of about 3.5617% due to daily compounding.
• The nominal rate alone isn't a sufficient measure; one has to consider how frequently interest is compounded.
• Higher frequency of compounding, as with daily compounding, doesn't always lead to the best interest reward.

Based on EARs, Bank A emerges as the better choice since it provides a higher effective return. However, if flexibility regarding withdrawals during the year is essential, Bank B might offer more convenience as interest accrues progressively throughout the year. Choosing the appropriate bank depends on your need for liquidity versus maximizing return.