This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# EffectiveInterest

 EffectiveInterest gives the effective interest rate corresponding to interest specification r, compounded at time intervals q.
• Symbolic expressions returned by EffectiveInterest can be solved for nominal rates, compounding periods or time parameters.
 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 gives the compounded average growth rate (CAGR) corresponding to the rate schedule .
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:
Effective rate corresponding to a nominal rate of 5% compounded 4 times per period:
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Schedule of nominal rates to effective rates, compounded 12 times per period:
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Convert a schedule of nominal rates to effective rates compounded 12 times per period:
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Compound annual growth rate (CAGR) corresponding to a schedule of rates:
 Out[1]=

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:
 Out[1]=

Solve for the nominal rate corresponding to an effective rate of 5% compounded quarterly:
 Out[1]=

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 Scope   (4)
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:
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: