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.

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

Where each payment is made at the beginning of a compounding period (for example, at the beginning of each year), the process is known as an "annuity due" or an "annuity in advance.

This chapter provides an extensive guide to basic time value formulas and concepts, including formulas for computing present values for future lump sums and annuities; future values for present lump sums and annuities; periodic payment values related to present and future lump sums; terms of years or number of periods related to present and future lump sums and annuities; and rate conversions, compounding periods, and effective interest rates.

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.

SS] = present value of a single sum i = interest rate (annual) m = number of

compounding periods n = number of years