EffectiveInterest
✖
EffectiveInterest
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:
-
r nominal 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.
Examples
open allclose allBasic Examples (7)Summary of the most common use cases
Effective rate corresponding to a nominal rate of 5% compounded 4 times per period:

https://wolfram.com/xid/0ywao0ysvmli-jgoxcf

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

https://wolfram.com/xid/0ywao0ysvmli-d3es81

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

https://wolfram.com/xid/0ywao0ysvmli-dapf6m

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

https://wolfram.com/xid/0ywao0ysvmli-o7c5j

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:

https://wolfram.com/xid/0ywao0ysvmli-lxfvji

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

https://wolfram.com/xid/0ywao0ysvmli-e55y2

Use EffectiveInterest with TimeValue:

https://wolfram.com/xid/0ywao0ysvmli-jw4ytn

Scope (5)Survey of the scope of standard use cases
A compounding interval of zero can be used to specify continuous compounding:

https://wolfram.com/xid/0ywao0ysvmli-fdj24

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:

https://wolfram.com/xid/0ywao0ysvmli-fd6cft

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

https://wolfram.com/xid/0ywao0ysvmli-c5g097

This is equivalent to the analogous simple interest computation:

https://wolfram.com/xid/0ywao0ysvmli-h15dkm

EffectiveInterest works with symbolic parameters:

https://wolfram.com/xid/0ywao0ysvmli-mdz6rz


https://wolfram.com/xid/0ywao0ysvmli-mkdx5


https://wolfram.com/xid/0ywao0ysvmli-pyv16i

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

https://wolfram.com/xid/0ywao0ysvmli-cho2xw

EffectiveInterest from a TimeSeries:

https://wolfram.com/xid/0ywao0ysvmli-gj3tuk

https://wolfram.com/xid/0ywao0ysvmli-iwkfmx

Generalizations & Extensions (1)Generalized and extended use cases
Applications (1)Sample problems that can be solved with this function
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:

https://wolfram.com/xid/0ywao0ysvmli-fcid5

Use FindRoot instead:

https://wolfram.com/xid/0ywao0ysvmli-d0j3gy

Neat Examples (1)Surprising or curious use cases
Wolfram Research (2010), EffectiveInterest, Wolfram Language function, https://reference.wolfram.com/language/ref/EffectiveInterest.html.
Text
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.
CMS
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. Wolfram Research. https://reference.wolfram.com/language/ref/EffectiveInterest.html.
APA
Wolfram Language. (2010). EffectiveInterest. Wolfram Language & System Documentation Center. Retrieved from 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
BibTeX
@misc{reference.wolfram_2025_effectiveinterest, author="Wolfram Research", title="{EffectiveInterest}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/EffectiveInterest.html}", note=[Accessed: 05-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_effectiveinterest, organization={Wolfram Research}, title={EffectiveInterest}, year={2010}, url={https://reference.wolfram.com/language/ref/EffectiveInterest.html}, note=[Accessed: 05-June-2025
]}