The main benefit of compound interest for savers is the promise of exponential growth of their money. Once interest is added to an account, it begins to earn interest itself, increasing the rate at which the account can grow. This applies to all types of savings instruments, including savings accounts, money market funds, and certificates of deposit (CDs). Lenders also benefit from compound interest, as unpaid interest added to the loan balance also earns additional interest, which increases the balance due.

If a savings deposit remains untouched except for the addition of interest, each of these deposits will be higher than the previous one and will eventually exceed the amount of the original deposit. Combined with a modest regular savings program, such an account can grow very quickly. This is what is meant when people talk about the "miracle of compound interest".

When money is borrowed or deposited, interest is earned on that amount – called the principal – which is essentially the cost of using the money. Interest is "simple" when it is not added to principal, and "compounded" when it is. Calculated as a percentage of the principal, it is usually expressed as the percentage paid over a period of time.

For example, a particular savings account may pay 5% annual interest, calculated and credited – or compounded – quarterly. If the annual interest is accrued on a period of less than one year, it is prorated, so that the quarterly interest rate of 5% annual interest is actually 1.Would be 25% of the principal amount. The 1 earned in the first quarter.25% is added to the principal amount and is the basis for calculating the interest payment for the second quarter, etc. However, savings instruments with a maturity of one year or less, like many CDs, generally pay only simple interest, which is calculated once at maturity and paid out with the principal to the owner.

Savings accounts and money market accounts, among others, generally accrue interest more frequently than CDs. The frequency with which interest is compounded is an important consideration when comparing accounts. When two accounts have equal interest rates, the account for which interest is accrued more frequently grows faster. For example, an account with a 5% annual interest rate that is compounded quarterly grows faster than an account whose interest is compounded every 6 months. However, some institutions charge interest very frequently, often daily, but credit the account less frequently, such as monthly or quarterly, somewhat dampening the compounding effect.

The method of calculating interest can vary from institution to institution. Some institutions base the calculation on the lowest balance during the calculation period – i.e., only the money that was in the account during the entire period. Another method is based on the average daily balance, while some institutions charge interest on the actual daily balance. All depositors, but especially those who use their account frequently, benefit most from daily interest calculation. The average daily balance is the next most advantageous method, while the lowest daily balance is the least advantageous.

Compound interest is also a feature of loans. When loans are made, the interest due is usually stated as an annual percentage rate payable each month. If interest due is paid on time, there is no compounding effect. However, if less than the full amount of interest due is paid, the unpaid amount begins to accrue interest itself at the beginning of the next period. This is a feature of revolving credit loans such as home equity lines of credit (HELOCs) and credit cards that is advantageous to lenders.