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.

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.

Frequently, financial planners and investors need to convert a rate quoted for one interval into an equivalent rate for another interval or to convert a rate determined for one compounding period into an equivalent rate for another compounding period.

For instance, most mortgages are generally paid monthly and the compounding period is also generally monthly.

Generally, of course, the calculation actually goes the other way where one knows the stated annual rate and wants to find the compounding period rate:

The safe harbor interest rate is 150% of the highest AFR, at the appropriate

compounding period in effect at any time beginning when the right to the guaranteed payment for capital is first established through the end of the tax year.

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.

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