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

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5 years, 9 months ago

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Ben Brawn 5 years, 9 months ago

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Ben Brawn 5 years, 9 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	8
period	list	[ "annually", 1, "year" ]
ipadec	number	0.06
ipa	number	6
C	integer	90
n	integer	8
F	number	890.7721117963
Frounded	number	890.77

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Generated value: `integer`

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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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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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future 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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future value - ordinary annuity

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Taxonomy: mathcentre

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Taxonomy: Context

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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

Parts

Gap-fill

Generated value: `integer`