# 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

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## Basic Examples(7)

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

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

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

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

 In:= Out= 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:

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

 In:= Out= Use EffectiveInterest with TimeValue:

 In:= Out= ## Neat Examples(1)

Introduced in 2010
(8.0)