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AnnuityDue
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AnnuityDue

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AnnuityDue[p,t]

represents an annuity due of fixed payments p made over t periods.

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AnnuityDue[p,t,q]

represents a series of payments occurring at time intervals q.

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AnnuityDue[{p,{pinitial,pfinal}},t,q]

represents an annuity due with the specified initial and final payments.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Present value of an annuity due of 10 payments of $1000 at 6% effective interest:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-epe6u9
Out[1]=1

Future value of an annuity due of 5 payments of $1000 at 8% nominal interest compounded quarterly:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-cgqs40
Out[1]=1

Future value of a 10-period annuity due with payments occurring twice per period:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-fhhx7m
Out[1]=1

Scope  (1)Survey of the scope of standard use cases

Infinity may be used as the number of payment periods to specify a perpetuity due:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-f5mzo5
Out[1]=1

Applications  (3)Sample problems that can be solved with this function

Value of a delayed annuity whose 7 payments start in 5 years:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-nxq0aj
Out[1]=1

At what annual effective interest is the present value of a series of payments of 1 every 6 months forever, with the first payment made immediately, equal to 10:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-6ys69
Out[1]=1

Find the accumulated value at the end of 10 years of an annuity in which payments are made at the beginning of each half-year for five years. The first payment is $2000, and each payment is 98% of the prior payment. Interest is credited at 10% compounded quarterly:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-ddd4vu
Out[1]=1

Properties & Relations  (1)Properties of the function, and connections to other functions

TimeValue takes a reference point argument for cash flows. This argument can be used with Annuity to simulate an annuity due:

In[1]:=1
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https://wolfram.com/xid/0v5xr31x64kjk-rg59e
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v5xr31x64kjk-c63wqm
Out[2]=2
Wolfram Research (2010), AnnuityDue, Wolfram Language function, https://reference.wolfram.com/language/ref/AnnuityDue.html.
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Wolfram Research (2010), AnnuityDue, Wolfram Language function, https://reference.wolfram.com/language/ref/AnnuityDue.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_annuitydue, author="Wolfram Research", title="{AnnuityDue}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/AnnuityDue.html}", note=[Accessed: 14-May-2025 ]}

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@misc{reference.wolfram_2025_annuitydue, author="Wolfram Research", title="{AnnuityDue}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/AnnuityDue.html}", note=[Accessed: 14-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_annuitydue, organization={Wolfram Research}, title={AnnuityDue}, year={2010}, url={https://reference.wolfram.com/language/ref/AnnuityDue.html}, note=[Accessed: 14-May-2025 ]}

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@online{reference.wolfram_2025_annuitydue, organization={Wolfram Research}, title={AnnuityDue}, year={2010}, url={https://reference.wolfram.com/language/ref/AnnuityDue.html}, note=[Accessed: 14-May-2025 ]}