Banks offer interestbearing accounts to consumers that allow savers to deposit money and earn interest on balance held. Interest compounding occurs when interest begins to accrue on previously accrued interest. Financial accounts can be subject to different compounding periods such as daily or monthly compounding. Daily compounding is more beneficial to savers than monthly compounding if all other factors are held equal.
Interest Compounding Basics

When a bank offers an interestbearing account, like a savings account, it will set a certain interest rate and compounding period. After the end of the compounding period, the bank adds earned interest to the account balance. This interest will begin to accrue on the new balance beginning in the next period. An account that compounds more often will grow more quickly because it earns interest on previously earned interest sooner, meaning daily compounding is better if you are saving money than monthly compounding.
Yearly, Monthly and Daily Compounding

If you save $100 in an account at a 10 percent annual rate that compounds yearly you will simply get $10 after saving for a year. If that same account compounded monthly, your balance would increase to $100.83  1/12 of 10 percent  after a month. For the rest of the year you would earn 10 percent interest on the extra 83 cents you earned in the first month. After the whole year you would have earned $10.47 in interest instead of $10. If the account compounded daily, a few fractions of a cent in interest accrues on your balance every day. If you saved $100 in an account at 10 percent interest that compounded daily you would have $110.52 after a year.
Annual Percentage Yield

When you shop for savings accounts, banks may quote the rates you see as annual percentage yields. The APY of an interest bearing account is the total annual interest you will receive, taking the impact of compounding into account. In other words, two savings accounts that both offer 5 percent APY will pay the same amount even if they use different compounding methods.
Considerations

The formula for calculating compound interest is A=P(1+r/n)^nt where A is the final account balance, P is the original principle, r is the interest rate, n is the number of compounding periods per year and t is the amount of time the money is saved in years. Many websites offer free compound interest calculators that will calculate end balances based on a principle amount and interest rate that you provide.