Patricia's copy of present value - ordinary annuity

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Patricia Cogan 4 years, 3 months ago

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Patricia Cogan 4 years, 3 months ago

Created this as a copy of present value - ordinary annuity.

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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			Name	Type	Generated Value

years	integer	15
period	list	[ "monthly", 12, "month" ]
ipadec	number	0.092
ipa	number	9.2
C	integer	190
n	integer	180
P	number	18514.9350171161
Prounded	number	18514.94

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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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Patricia's copy of present value - ordinary annuity

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Patricia Cogan 4 years, 3 months ago

Patricia Cogan 4 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Patricia's copy of present value - ordinary annuity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Patricia Cogan 4 years, 3 months ago

Patricia Cogan 4 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`