Compound Interest Formulas - Savings

When interest is added to the principal amount of deposit, and then subsequent periods of interest earnings are based on the principal and interest amounts for the prior period(s) combined there is said to be compound interest. This compounding raises the level of earnings over simple interest methods. The following are based on (1) year periods.

Daily compounding over a year=
Principal Deposit (1+ % interest rate/365)³⁶⁵


Monthly compounding over same =
Principal Deposit (1+ % interest rate/12)¹²


Quarterly compounding over ditto =
Principal Deposit (1+ % interest rate/4)⁴


While the above are for single year periods, the exponent changes when accounting for other periods. To illustrate this point, monthly compounding over a 3 year period at 3% per annum looks like:

Principal Deposit (1.0025)³⁶


Where the period number, 36, is gotten by: 3x12mo.'s = 36


And the rate of interest arrived at by: 3/12 = .25% = .0025


As you can see, the main variable is the period of compounding. Try for yourself and you will notice that the more often the periods of compounding occur, the increased the rates of return that go to the account holder. Although this much depends on the advertised rates from the bank, frequency of compounding could potentially factor against the increase in the rate of return. It therefore deserves further analysis based on the rates and compounding cycles being offered.

Quickly figure compound interest with our compound interest calculator.

Continuous compounding, used to describe compounding that is computed continuously over periods, generally goes to the benefit of the depositor, at least by itself in concept. On another side of a coin, it might not be so advantageous for someone held to making loan payments.

Quickly calculate continuously compounded interest.