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Cashflow [{c0,c1,,cn}]

represents a series of cash flows occurring at unit time intervals.

Cashflow [{c0,c1,,cn},q]

represents cash flows occurring at time intervals q.

Cashflow [{{time1,c1},{time2,c2},}]

represents cash flows occurring at the specified times.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
Interactive Examples  
Neat Examples  
See Also
Related Guides
History
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Cashflow [{c0,c1,,cn}]

represents a series of cash flows occurring at unit time intervals.

Cashflow [{c0,c1,,cn},q]

represents cash flows occurring at time intervals q.

Cashflow [{{time1,c1},{time2,c2},}]

represents cash flows occurring at the specified times.

Details

  • TimeValue [Cashflow[],interest,t] computes the time value of a cash flow as a single equivalent payment at the specified time t. Possible cash flow calculations include net present value, discounted cash flow, and internal rate of return.
  • Times and amounts can be given as numbers or arbitrary symbolic expressions.
  • In Cashflow [{{time1,c1},}], the timei can be given as numerical values or date expressions.
  • Cashflow [{c0,c1,c2,}] is equivalent to Cashflow [{{0,c0},{1,c1},{2,c2},}].
  • TimeValue [Cashflow[{{date0,c0},}],r,date] computes the time value of a cash flow at date.
  • Cashflow [Annuity []] converts an Annuity object to a Cashflow object.

Examples

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Basic Examples  (4)

Compute the present value at 7% of a stream of cash flows occurring at regular time intervals:

Specify an interval at which cash flows occur:

Future value at 9% of a stream of cash flows occurring at irregular time intervals:

Find the net present value of a 1000ドル initial investment producing future incoming cash flows:

Scope  (6)

Convert an Annuity object to a Cashflow object:

Cashflow works with date expressions:

Specify Cashflow with a TimeSeries :

Cashflow works with symbolic parameters:

Solutions to equations involving Cashflow can be found in terms of symbolic parameters:

Calculate the duration of a series of cash flows using the derivative function D :

Applications  (6)

Internal rate of return of an investment with regular cash flows:

Find the payment at time 2 that will make the net present value of a series of cash flows zero:

Solve for the point in time where a payment of 400ドル will make the net present value equal to 0:

In return for receiving 600ドル at the end of 8 years, a person pays 100ドル immediately, 200ドル at the end of 5 years and a final payment at the end of 10 years. Find the final payment amount that will make the rate of return on the investment equal to 8% compounded semiannually:

Payments of 100,ドル 200ドル and 500ドル are due at the end of years 2, 3 and 8, respectively. Find the point in time where a payment of 800ドル would be equivalent at 5% interest:

Find the effective rate of interest at which the present value of 2000ドル at the end of 2 years and 3000ドル at the end of 4 years will be equal to 4000ドル:

Properties & Relations  (3)

A Cashflow object with one cash flow is equivalent to a simple amount:

Large cash flow sequences that obey a pattern can be generated through Annuity using a payment growth function:

Large cash flow streams can also be created using Table :

Use Plot and Plot3D to explore the various dependencies a series of cash flows has on a set of variables:

Dependence on interest rate:

Dependence on payment growth rate:

Use Plot3D to view the interest rate/growth rate landscape:

Possible Issues  (2)

When specifying a valuation period in between payments of a Cashflow object, TimeValue calculates the future value of all cash flows before the valuation period, and the present value of all cash flows after the valuation period:

This is equivalent to the sum of present and future values here:

Cashflow [Annuity [pmt,n,q]] only works for numeric n and f:

Using numeric n allows Cashflow to convert the Annuity object as desired:

Interactive Examples  (1)

Use Manipulate to explore the various dependencies a series of cash flows has on a set of variables:

Neat Examples  (1)

Plot the cash flows in a "sawtooth"-style cash flow stream together with the accumulated value as a function of time:

Wolfram Research (2010), Cashflow, Wolfram Language function, https://reference.wolfram.com/language/ref/Cashflow.html.

Text

Wolfram Research (2010), Cashflow, Wolfram Language function, https://reference.wolfram.com/language/ref/Cashflow.html.

CMS

Wolfram Language. 2010. "Cashflow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Cashflow.html.

APA

Wolfram Language. (2010). Cashflow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cashflow.html

BibTeX

@misc{reference.wolfram_2025_cashflow, author="Wolfram Research", title="{Cashflow}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Cashflow.html}", note=[Accessed: 04-January-2026]}

BibLaTeX

@online{reference.wolfram_2025_cashflow, organization={Wolfram Research}, title={Cashflow}, year={2010}, url={https://reference.wolfram.com/language/ref/Cashflow.html}, note=[Accessed: 04-January-2026]}

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