cash flow amount - ordinary perpetuity - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Ben Brawn

Feedback

From users who are members of ACFI1003 :

Ben Brawn

said

Ready to use

5 years, 9 months ago

History

○

Ben Brawn 5 years, 9 months ago

Gave some feedback: Ready to use

○

Ben Brawn 5 years, 9 months ago

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

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

There are 8 other versions that do you not have access to.

Question statement

If you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again. Do each question repeatedly to ensure you have mastered it.

Give any introductory information the student needs.

			Name	Type	Generated Value

period	list	[ "yearly", 1, "year" ]
ipadec	number	0.085
ipa	number	8.5
P	integer	5000
C	number	425
Crounded	number	425.00

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.

Can an exam override the value of this variable?

Generated value: `list`

[ "yearly", 1, "year" ]

→ Used by:

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Suppose you want to set up a scholarship or a donation that gives a regular amount at the end of every {period[2]} forever. If you have $\$\var{P}$ to invest at $\var{ipa}\%$ p.a. compounded {period[0]}, what amount would be given each {period[2]}?

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

Advice

You are asked to find the cash flow amount 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,

$P=\var{P}$ ,

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

and therefore we have

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

which we need to rearrange to solve for $C$ .

We multiply both sides by $\left(\simplify[unitDenominator]{{ipadec}/{period[1]}}\right)$ (to remove the division by it)

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

Calculating this we find

$C=\$\var{Crounded}\quad \text{(to the nearest cent)}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
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.

Loading...

Error

cash flow amount - 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

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

cash flow amount - 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

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`