present value - ordinary perpetuity - 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

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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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Question statement

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			Name	Type	Generated Value

period	list	[ "quarterly", 4, "quarter" ]
ipadec	number	0.039
ipa	number	3.9
C	integer	50
P	number	5128.2051282051
Prounded	number	5128.21

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random([random('yearly','annually'),1,'year'],[random('half-yearly','semiannually'),2,'half-year'],['quarterly', 4, 'quarter'],['monthly',12,'month'],['daily', 365,'day'])

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ "quarterly", 4, "quarter" ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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Suppose you want to set up a scholarship or a donation that gives $\$\var{C}$ at the end of every {period[2]} forever. If you could invest at $\var{ipa}\%$ p.a. compounded {period[0]}, what amount would you need to invest at the start to ensure the cash flow lasts forever.

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

Advice

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

$\displaystyle P=\frac{C}{i}$

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

In our situation we have,

$C=\var{C}$ ,

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

and therefore we have

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

Calculating this we find

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

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Ordinary perpetuity 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 perpetuity

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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: `list`

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present value - ordinary perpetuity

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: list

Parts

Gap-fill

Generated value: `list`