BUILT-IN MATHEMATICA SYMBOL

# EffectiveInterest

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

## Details and OptionsDetails 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 .
• EffectiveInterest[{p1->r1, p2->r2, ...}] gives the equivalent schedule of future spot rates.

## ExamplesExamplesopen allclose all

### Basic Examples (7)Basic Examples (7)

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

 Out[1]=

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

 Out[1]=

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

 Out[1]=

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]=

Use EffectiveInterest with TimeValue:

 Out[1]=