Patricia's copy of cash flow amount - annuity due

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Patricia Cogan 4 years, 1 month ago

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Patricia Cogan 4 years, 1 month ago

Created this as a copy of cash flow amount - annuity due.

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 borrow $\$\var{P}$ to buy a house. The term of the loan is $\var{years}$ years, and you will need to make {period[0]} repayments on the loan at the beginning of each {period[2]}. Interest is $\var{ipa}\%$ per annum compounding {period[0]}.

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			Name	Type	Generated Value

years	integer	20
period	list	[ "monthly", 12, "month" ]
ipadec	number	0.0112
ipa	number	1.12
n	integer	240
P	integer	356000
C	number	1654.8085384319
Crounded	number	1654.81

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Which formula should you use to calculate the size of your monthly repayment?

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

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

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Advice

You are asked to find the repayment amount of an annuity due (since the payments are at the beginning of each period) and we are given the present value of the annuity. Therefore we will use the present value of an annuity due formula

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

where $P$ is the present value, $R$ is the repayment per period, $i$ is the interest rate per period, and $n$ is the number of periods.

In our situation we have,

$P=\var{P}$ ,

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

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

and therefore we have

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

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

Calculating this we find

$\begin{align}R&\approx \var{C}\\&=\$\var{Crounded}\quad \text{(to the nearest cent)}\end{align}$

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Patricia's copy of cash flow amount - annuity due

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Patricia Cogan 4 years, 1 month ago

Patricia Cogan 4 years, 1 month ago

Error in variable testing condition

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Patricia's copy of cash flow amount - annuity due

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Patricia Cogan 4 years, 1 month ago

Patricia Cogan 4 years, 1 month ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`