Future Value - Annuity 1 - Numbas at mathcentre.ac.uk

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Name	Status	Author	Last Modified
Future Value - Annuity 1	Ready to use	Julie Crowley	07/10/2016 22:23
Simon's copy of Future Value - Annuity 1	draft	Simon Thomas	30/05/2019 12:23

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Question statement

To provide for retirement an employee deposits € $\var{R}$ at the end of each month into an account that earns $\var{perc}$ % annual interest compounded monthly.

Give any introductory information the student needs.

			Name	Type	Generated Value

R	integer	60
perc	number	9
perc2	number	0.75000
int	number	0.0075
num	number	1.8732019633
years	integer	7
n	integer	84
num2	number	0.8732019633
num3	number	116.4269284462
A	number	6985.62

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What is the future value of the annuity in $\var{years}$ years?

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The future value of an annuity, $A$ is given by:

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

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

$A$ represents the future 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:

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

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

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

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

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

$A=\var{A}$

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Future Value - Annuity 1

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Julie Crowley 8 years, 7 months ago

Julie Crowley 8 years, 11 months ago

Julie Crowley 9 years, 1 month ago

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Generated value: `integer`

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Future Value - Annuity 1

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

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Warning

Generated value: integer

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Generated value: `integer`