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Finance

 effectiverate
 convert a stated rate to the effective rate

 Calling Sequence effectiverate(stated_rate, nperiods)

Parameters

 stated_rate - interest rate, expressed as a decimal number nperiods - number of times the rate is compounded in the period

Description

 • Continuous compounding is indicated by specifying infinity as the number of compounding periods.
 • Since effectiverate used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[effectiverate]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[effectiverate].

Examples

A given loan is at 12% compounded monthly. The effective rate is then 1% monthly compounded 12 times. One can calculate it as follows:

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{effectiverate}\left(0.12,12\right)$
 ${0.126825030}$ (1)

or about 12.7%. This can also be seen as:

 > ${\left(1+\frac{0.12}{12}\right)}^{12}-1$
 ${0.126825030}$ (2)

Compounded continuously, the effective rate is:

 > $\mathrm{effectiverate}\left(0.12,\mathrm{∞}\right)$
 ${0.127496852}$ (3)

Compatibility

 • The Finance[effectiverate] command was introduced in Maple 15.