present value - ordinary annuity - Numbas at mathcentre.ac.uk

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Name	Status	Author	Last Modified
present value - ordinary annuity	Ready to use	Ben Brawn	21/06/2019 03:29
future value - ordinary annuity	Ready to use	Ben Brawn	21/06/2019 03:29
future value - annuity due	Ready to use	Ben Brawn	26/06/2019 09:26
present value - annuity due	Ready to use	Ben Brawn	21/06/2019 03:24
cash flow amount - ordinary annuity	Ready to use	Ben Brawn	21/06/2019 03:29
cash flow amount - annuity due	Ready to use	Ben Brawn	21/06/2019 03:22
present value - ordinary perpetuity	Ready to use	Ben Brawn	21/06/2019 03:36
cash flow amount - ordinary perpetuity	Ready to use	Ben Brawn	21/06/2019 03:36
interest rate - ordinary perpetuity	Ready to use	Ben Brawn	21/06/2019 03:37
future value - ordinary annuity	draft	Xiaodan Leng	10/07/2019 21:31
present value - deferred annuity	Ready to use	Ben Brawn	11/03/2022 00:42
Patricia's copy of cash flow amount - annuity due	draft	Patricia Cogan	30/01/2024 10:47
Patricia's copy of future value - ordinary annuity	draft	Patricia Cogan	30/01/2024 10:42
Patricia's copy of present value - ordinary annuity	draft	Patricia Cogan	25/01/2021 22:29

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Question statement

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			Name	Type	Generated Value

years	integer	17
period	list	[ "daily", 365, "day" ]
ipadec	number	0.041
ipa	number	4.1
C	integer	3
n	integer	6205
P	number	13404.4880756291
Prounded	number	13404.49

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Suppose you are given $\$\var{C}$ at the end of each {period[2]} for $\var{years}$ years. If the interest rate is $\var{ipa}\%$ per annum compounding {period[0]}, what is this cash flow worth at the beginning of the $\var{years}$ years?

$\$$ Unnamed gap (to the nearest cent)

Advice

You are asked to find the present value of an ordinary annuity (since the payments are at the end of each period). Therefore we will use the present value of an ordinary annuity formula

$\displaystyle P=\frac{C}{i}\left(1-\frac{1}{(1+i)^n}\right)$

where $P$ is the present value, $C$ is the cash flow per period, $i$ is the interest rate per period, and $n$ is the number of periods.

In our situation we have,

$C=\var{C}$ ,

$i=\frac{\var{ipa}\%}{\var{period[1]}}=\frac{\var{ipadec}}{\var{period[1]}}$ , $i=\var{ipa}\%=\var{ipadec}$ ,

$n=\var{years}\times \var{period[1]}=\var{n}$ , $n=\var{n}$ ,

and therefore we have

$\displaystyle P=\frac{\var{C}}{\left(\simplify[unitDenominator]{{ipadec}/{period[1]}}\right)}\left(1-\frac{1}{\left(1+\simplify[unitDenominator]{{ipadec}/{period[1]}}\right)^\var{n}}\right)$

Calculating this we find

$\begin{align}P&\approx \var{P}\\&=\$\var{Prounded}\quad \text{(to the nearest cent)}\end{align}$

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This question is used in the following exams:

Ordinary annuity by Ben Brawn in ACFI1003.
Five randomly selected financial maths questions by Ben Brawn in ACFI1003.
Practice Finance Calculations by Ben Brawn in ACFI1003.

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present value - ordinary annuity

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Ben Brawn 5 years, 9 months ago

Ben Brawn 5 years, 9 months ago

Ben Brawn 5 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

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present value - ordinary annuity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn 5 years, 9 months ago

Ben Brawn 5 years, 9 months ago

Ben Brawn 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`