EffectiveInterest
EffectiveInterest[r,q]
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)
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)
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:
Text
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.
APA
Wolfram Language. (2010). EffectiveInterest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EffectiveInterest.html