Present value - Annuity 2 - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Julie Crowley

Feedback

From users who are members of Julie's workspace :

Julie Crowley

said

Ready to use

8 years, 11 months ago

History

○

Julie Crowley 8 years, 7 months ago

Published this.

○

Julie Crowley 8 years, 11 months ago

Gave some feedback: Ready to use

○

Julie Crowley 9 years, 1 month ago

Created this as a copy of Present value - Annuity 2.

Name	Status	Author	Last Modified
Present value - Annuity 2	Ready to use	Julie Crowley	07/10/2016 22:24
Simon's copy of Present value - Annuity 2	draft	Simon Thomas	30/05/2019 11:52

There are 6 other versions that do you not have access to.

Question statement

A $\var{years}$ -year lease for a company car requires a payment of € $\var{R}$ at the end of each month.

The formula for calculating the present value ( $P$ ) of an annuity is:

$P=\frac{R[1-(1+i)^{-n}]}{i}$

where $R$ represents the value of each repayment, $i$ represents the interest rate and $n$ represents the number repayments.

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

perc	number	5.5
int	number	0.0045833
P	number	9935.13
n	integer	36
R	integer	300
Interest	number	864.87
num	number	0.8482144111
perc2	number	0.45833
num2	number	0.1517855889
num3	number	33.1170966168
years	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(4.5..8.5#0.5)

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: `number`

5.5

This variable doesn't seem to be used anywhere.

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.

Find the present value of these payments if the annual interest rate is $\var{perc}$ % compounded monthly. Give your answer to the nearest cent.

€Unnamed gap

Advice

The present value of an annuity, $P$ is given by:

$P=\frac{R[1-(1+i)^{-n}]}{i}$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

$P$ represents the present value of the annuity, this is what we are asked to calculate.

$i$ represents the rate of compound interest. the annual interest rate is $\var{perc}$ % so the monthly rate of interest is $\frac {\var{perc}} {12}=\var{perc2}$ % and therefore $i=\frac{\var{perc2}}{100}=\var{int}$ .

$n$ represents the number of payments, there are 12 payments over $\var{years}$ year(s) so $n$ is $12 \times \var{years}=\var{n}$ .

The value of each repayment, is € $\var{R}$

Using the formula:

$P=\frac{R[1-(1+i)^{-n}]}{i}$

$P=\frac{\var{R}[1-(1+\var{int})^{-\var{n}}]}{\var{int}}$

$P=\frac{\var{R}[1-\var{num}]}{\var{int}}$

$P=\frac{\var{R}[\var{num2}]}{\var{int}}$

$P = \var{R} \times \var{num3}$

$P=\var{P}$

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:

Loading...

Error

Present value - Annuity 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julie Crowley 8 years, 7 months ago

Julie Crowley 8 years, 11 months ago

Julie Crowley 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Present value - Annuity 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julie Crowley 8 years, 7 months ago

Julie Crowley 8 years, 11 months ago

Julie Crowley 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`