On the other hand, Investopedia defines compound interest as interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loanThe rate at which compound interest accrues depends on the frequency of compounding; the higher the number of

compounding periods, the greater the compound interest.

This idea is used if the number of

compounding periods per year is infinitely high.

Where the number of compounding periods differs from the number of payment periods, to compare alternative investments it is sometimes necessary to convert the stated interest rates to equivalent effective interest rates.

A further shortcoming of tables is evident when, for example, the interest rate or the compounding period is more complex (such as an interest rate of 10.375%, or a compounding period of 20 years, 7 months).

In this case the formula would be needed to arrive at the actual compounding period required.

The following sections present basic time value formulas for computing present values, future values, payments for annuities, the number of periods or the term, rates of return, and interest rate conversions, compounding periods, and effective interest rates, with examples.

The values of the number of compounding periods, c, and for the number of payment periods, p, are often the same, but they need not be.

The "stated annual rate" is usually defined as the compounding rate per period times the number of compounding periods per year.

That is, no matter how many

compounding periods into which the year is divided, it will never exceed the value of 2.718282 07 = 1.072508.

Formula: [FV.sub.SS] = [PV.sub.SS] [(1 + i/m).sup.mn] [FV.sub.SS] = future value of a single sum [PV.sub.SS] = present value of a single sum i = interest rate (annual) m = number of

compounding periods n = number of years

The nominal rate may be used in a financial calculator because the calculator can automatically adjust for the compounding period (payment frequency).

In order for the TVM equation to be accurate, the rate needs to reflect the semi-monthly compounding period.