Patricia's copy of present value - ordinary annuity

Error

There was an error loading the page.

Contributors

History

○

Patricia Cogan 4 years, 2 months ago

Published this.

○

Patricia Cogan 4 years, 2 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

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

years	integer	9
period	list	[ "annually", 1, "year" ]
ipadec	number	0.084
ipa	number	8.4
C	integer	300
n	integer	9
P	number	1843.2905362583
Prounded	number	1843.29

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..20)

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: `integer`

→ Used by:

Advice
"Unnamed part" - prompt

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

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

Advice

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

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

where $P$ is the present 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

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

Calculating this we find

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

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 not used in any exams.

Loading...

Error

Patricia's copy of present value - ordinary annuity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Patricia Cogan 4 years, 2 months ago

Patricia Cogan 4 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Patricia's copy of present value - ordinary annuity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Patricia Cogan 4 years, 2 months ago

Patricia Cogan 4 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`