BUILT-IN MATHEMATICA SYMBOL

EffectiveInterest

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

MORE INFORMATION

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, 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 returns an expression in the same form as r.

EffectiveInterest specifies continuous compounding.

EffectiveInterest gives the compounded average growth rate (CAGR) corresponding to the rate schedule .

EffectiveInterest 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:

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:

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:

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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:

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

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Use EffectiveInterest with TimeValue:

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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:

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: