# TimeValue

TimeValue[s,i,t]

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

# Details 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 t1 to t using interest i. Time t1 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 {r1,r2,}, where the ri are interest rates for consecutive unit periods.
• {r0,{t1,r1},{t2,r2},} specifies an interest rate in effect before time t1. 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

# Examples

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## 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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## Interactive Examples(1)

Introduced in 2010
(8.0)