BUILT-IN MATHEMATICA SYMBOL

# TimeValue

TimeValue[s, i, t]
calculates the time value of a security s at time t for an interest specified by i.

## Details and OptionsDetails and Options

• For a simple amount a and an effective interest rate i, TimeValue[a, i, t] gives the future or accumulated value of a at time t.
• TimeValue[a, i, -t] gives the present or discounted value of a simple amount a for an effective interest rate i.
• Times can be given in abstract units or as dates.
• TimeValue works with arbitrary numeric or symbolic expressions. Symbolic formulas returned by TimeValue can be solved for interest rates, payments, or time periods using built-in functions such as Solve and FindRoot.
• In TimeValue[s, ...], the security s can be given as a simple amount or as a Cashflow, Annuity, or AnnuityDue object.
• TimeValue[s, i, {t, t1}] computes the time value accumulated or discounted from time to t using interest i. Time serves as a reference point for cash-flow occurrences.
• TimeValue[s, i] is equivalent to TimeValue[s, i, 0].
• TimeValue[..., t] is equivalent to TimeValue[..., {t, 0}].
• In TimeValue[s, i, t], the interest i can be specified in the following forms:
•  r effective interest rate {r1,r2,...} schedule of rates applied over unit time intervals {{t1,r1},{t2,r2},...} schedule of rates changing at the specified time {p1->r1,p2->r2,...} term structure of effective interest rates function force of interest, given as a function of time EffectiveInterest[...] an EffectiveInterest object
• TimeValue[s, EffectiveInterest[r, 1/n], t] uses a nominal interest rate r, compounded n times per unit period. If times are specified as concrete dates, all interest rates are assumed to be annual rates.
• TimeValue[s, {r1, r2, ...}, ...] gives the time value of an asset s for an interest rate schedule , where the are interest rates for consecutive unit periods.
• specifies an interest rate in effect before time . This is equivalent to {{-Infinity, r0}, {t1, r1}, {t2, r2}, ...}.
• TimeValue[security, {r1, r2, ...}, t] is equivalent to TimeValue[security, {{0, r1}, {1, r2}, ...}, t].
• TimeValue[a, f, {t, t1}] gives the time value of the simple amount a based on the force of interest function f which corresponds to the growth or decay process given by .
• A force of interest specification can be used with any security type.
• The following options can be given:
•  Assumptions \$Assumptions assumptions made about parameters GenerateConditions False whether to generate conditions on parameters

## ExamplesExamplesopen allclose all

### Basic Examples (14)Basic Examples (14)

Future value of \$1000 at an effective interest rate of 5% after 3 compounding periods:

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Present value of \$1000 at 5% over 3 periods:

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Future value of \$1000 using a nominal rate of 5% with quarterly compounding:

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TimeValue works with symbolic parameters:

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Present value at 6% of a 12-period annuity with payments of \$100:

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Future value at 6% of a series of cash flows occurring at regular intervals:

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Future value in three years' time of \$1000 invested on January 1, 2010 at 7.5%:

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Number of periods required to grow \$1000 to \$3000 at a 6% interest rate:

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Solve for the interest rate:

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Future value after 5 periods using a schedule of rates over unit time intervals:

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Present value using a schedule of rates effective at the specified times:

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Present value of an amount paid at time 10 using a term structure of interest rates:

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Future value using a schedule of rates over irregular time intervals:

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Compute the future value after three time periods using a force of interest :

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