Patricia's copy of future value - ordinary annuity

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Patricia Cogan 4 years, 2 months ago

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Patricia Cogan 4 years, 2 months ago

Created this as a copy of future 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

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Question statement

Suppose you are given $\$\var{C}$ to deposit into a savings account at the end of each {period[2]} for $\var{years}$ years. If the interest rate is $\var{ipa}\%$ per annum compounding {period[0]}, how much money is in the savings account after $\var{years}$ years?

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			Name	Type	Generated Value

years	integer	12
period	list	[ "monthly", 12, "month" ]
ipadec	number	0.026
ipa	number	2.6
C	integer	130
n	integer	144
F	number	21941.6205871293
Frounded	number	21941.62

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Which formula should we use to calculate the future value of the annuity in $\var{years}$ years?

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

Marks: Distractor Message:
$\displaystyle P=R \left [\frac{1-(1+i)^{-n}}{i} \right ]$

Marks: Distractor Message:
$\displaystyle P=R(1+i) \left[ \frac{1-(1+i)^{-n}}{i} \right]$

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

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Advice

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

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

where $A$ is the future value, $R$ is the amount deposited per period, $i$ is the interest rate per period, and $n$ is the number of periods.

In our situation we have,

$R=\var{C}$ ,

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

$n=\var{years}\times \var{period[1]}=\var{n}$ , $n=\var{n}$ ,

and therefore we have

$\displaystyle A=\var{C}(\frac{(1+\frac{\var{ipadec}}{\var{period[1]}})^\var{n}-1}{\frac{\var{ipadec}}{\var{period[1]}}})$

Calculating this we find

$\begin{align}A&\approx \var{F}\\&=\$\var{Frounded}\quad \text{(to the nearest cent)}\end{align}$

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Patricia's copy of future value - ordinary annuity

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Patricia Cogan 4 years, 2 months ago

Patricia Cogan 4 years, 2 months ago

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Patricia's copy of future value - ordinary annuity

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Taxonomy: mathcentre

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Patricia Cogan 4 years, 2 months ago

Patricia Cogan 4 years, 2 months ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`