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

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Xiaodan Leng 5 years, 8 months ago

Created this as a copy of future 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	9
period	list	[ "quarterly", 4, "quarter" ]
ipadec	number	0.067
ipa	number	6.7
C	integer	90
n	integer	36
F	number	4397.8477524657
Frounded	number	4397.85

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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 end of the $\var{years}$ years?

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

Advice

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

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

where $F$ is the future 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

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

Calculating this we find

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

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future value - ordinary annuity

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Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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future value - ordinary annuity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

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Warning

Generated value: integer

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Generated value: `integer`