gives the effective interest rate corresponding to interest specification r, compounded at time intervals q.

Details and Options

  • EffectiveInterest returns an expression suitable for use in TimeValue.
  • EffectiveInterest works with numerical or arbitrary symbolic expressions.
  • Symbolic expressions returned by EffectiveInterest can be solved for nominal rates, compounding periods, or time parameters.
  • In EffectiveInterest[r,q], the interest r can be specified in the following forms:
  • rnominal interest rate
    {r1,r2,}schedule of rates applied over unit time intervals
    {{t1,r1},{t2,r2},}schedule of forward rates changing at the specified times
    {p1->r1,p2->r2,}term structure of interest rates
  • EffectiveInterest[r,q] returns an expression in the same form as r.
  • EffectiveInterest[r,0] specifies continuous compounding.
  • EffectiveInterest[{r1,r2,}] gives the compounded average growth rate (CAGR) corresponding to the rate schedule {r1,r2,}.
  • EffectiveInterest[{p1->r1,p2->r2,}] gives the equivalent schedule of future spot rates.


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Basic Examples  (7)

Effective rate corresponding to a nominal rate of 5% compounded 4 times per period:

Schedule of nominal rates to effective rates, compounded 12 times per period:

Convert a schedule of nominal rates to effective rates compounded 12 times per period:

Compound annual growth rate (CAGR) corresponding to a schedule of rates:

Convert a term structure of interest rates (yield curve) to a list of implied forward rates and the corresponding intervals over which they are valid:

Solve for the nominal rate corresponding to an effective rate of 5% compounded quarterly:

Use EffectiveInterest with TimeValue:

Scope  (5)

A compounding interval of zero can be used to specify continuous compounding:

An integral compounding frequency may be used to specify compounding of less than once per period. As expected, the effective rate in this case is less than the nominal rate:

Simple interest can be simulated by using an integral compounding interval equal to the growth period:

This is equivalent to the analogous simple interest computation:

EffectiveInterest works with symbolic parameters:

Solutions to equations involving EffectiveInterest can be found in terms of symbolic parameters:

EffectiveInterest from a TimeSeries:

Generalizations & Extensions  (1)

Study the convergence of the future value of an amount as interest compounding approaches infinity:

Applications  (1)

Lender A quotes the nominal interest rate on a loan at 8% per year with continuous compounding. Lender B quotes their rate using quarterly compounding. Convert lender A's rate to an equivalent rate with quarterly compounding so that the two rates may be compared:

Use FindRoot instead:

Neat Examples  (1)

Study the convergence (to continuous compounding) of a nominal rate compounded at increasing frequencies:

Wolfram Research (2010), EffectiveInterest, Wolfram Language function, https://reference.wolfram.com/language/ref/EffectiveInterest.html.


Wolfram Research (2010), EffectiveInterest, Wolfram Language function, https://reference.wolfram.com/language/ref/EffectiveInterest.html.


Wolfram Language. 2010. "EffectiveInterest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EffectiveInterest.html.


Wolfram Language. (2010). EffectiveInterest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EffectiveInterest.html


@misc{reference.wolfram_2024_effectiveinterest, author="Wolfram Research", title="{EffectiveInterest}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/EffectiveInterest.html}", note=[Accessed: 17-June-2024 ]}


@online{reference.wolfram_2024_effectiveinterest, organization={Wolfram Research}, title={EffectiveInterest}, year={2010}, url={https://reference.wolfram.com/language/ref/EffectiveInterest.html}, note=[Accessed: 17-June-2024 ]}