interest rate - ordinary perpetuity - Numbas at mathcentre.ac.uk

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Ben Brawn

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Ben Brawn

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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 cash flow amount - 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

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Question statement

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			Name	Type	Generated Value

period	list	List of 3 items
seed	number	0.0545
P	integer	67000
C	number	1800
ippdec	number	0.0268656716
ipadec	number	0.0537313433
ipa	number	5.3731343284
iparounded	number	5.37

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`

[ "half-yearly", 2, "half-year" ]

→ Used by:

C
ipadec

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Number entry
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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 have $\$\var{P}$ to invest and the interest is compounded {period[0]} what would the nominal interest rate need to be?

Unnamed gap $\%$ p.a. (to 2 decimal places)

Advice

You are asked to find the nominal interest rate 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,

$P=\var{P}$ ,

$C=\var{C}$ ,

and therefore we have

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

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

We multiply both sides by $i$ (so that $i$ isn't in the denominator)

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

Then divide both sides by $\var{P}$ (to remove the multiplication by it)

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

Recall that $i$ is the interest rate per time period but we were asked for the interest rate per annum so we multiply by $\var{period[1]}$ to get

$\begin{array}\displaystyle \text{interest rate pa}&=\var{period[1]}\times \frac{\var{C}}{\var{P}}\\&\approx\var{ipadec}\\&=\var{iparounded}\%\quad \text{(2 decimal places)}\end{array}$

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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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interest rate - 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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interest rate - 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`