34413697 12 Mathematics a Applied Geometry Financial Maths

7/29/2019 34413697 12 Mathematics a Applied Geometry Financial Maths

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12 Mathematics AApplied Geometry, Financial Maths

12 Mathematics A, Page 1


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Sam Petherbridge 2010


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Part ATask 1


The drawing to the

left is not to scale.

For a scale version

please see the

back of the

assignment.


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Task 2

Task 3

Area = Length Width

=26m 14m

=364m2

The total floor space = 364m 2

Average building cost per square meter can be calculated from the

Mater Builders statistic that say's on average it will cost $300949

for a 200 square meter house.

The Average Cost Per Square Meter =$300949

200m2

=1504.745

1504.75

The Average Cost Per Square Meter $1504.75

From this we can calcualte the cost of building my dream home.

Cost of Building = The Total Floor Space The Average Cost Per Square Meter

=364m2 $1504.745

=547727.18

The cost of buliding my dream house = $547727.18



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Task 4


20/04/10 9:06 PMHighgate Hill, contact agent - Residential Land for Sale #2748483 - realestate.com.au

Page 1 of 1http://realestate.com.au/property-residential+land-qld-highgate+hill-2748483

Buy

copyright REA Group Ltd.

Residential Land

Highgate Hill, contact agent

$2,250,000

Open For Inspection Times

Inspect by appointment, contact agent.

Property No. 2748483

Page Visits: 62

Floorplans & Interactive Tours

Details not provided

View market trends for Highgate Hill

Property Description

DEVELOPERS DREAMThis is a unique opportunity for the astute developer or investor to secure a rare 1616sqm

allotment, (2 lots) with LMR Zoning in one of the most prestigious positions in Brisbane. This site offers uninterrupted views

over Highgate Hill , West End, the St Lucia reach of the river, Toowong and Mt Cootha on the horizon. The photos tell the

story. Ring Me now for an inspection. This is not to be missed. Phone John Fox on 0413603117

Suburb Information for Highgate Hill

John Fox

RE/MAX Advantage - Wynnum

128 Bay Terrace

Wynnum 4178

0413 603 117

[email protected]

Property Features & Amenities

General Features

Property Type: Residential LandLand Size: 1,616 m!

20 km

10 mi

Map data 2010 MapData Sciences Pty Ltd, PSMA -


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Task 5

Task 6

Transfer Duty = $37125 + (2250000-980000)100

$5.25

=$37125 +1270000

100

$5.25

=$37125 + 12700 $5.25( )=$37125 + $66675

=$103800

The Transfer Duty =$103800

Total Cost = Building Costs + Land Cost + Transfer Duty

=$547727.18 + $2250000 + $103800

=$2901527.18

Total Bank Loan Needed = Total Cost - 10% Deposit

= Total Cost - Total Cost 10%( )

=2901527.18- 2901527.18 0.10( )

=2901527.18-290152.718

=2611374.46

The Amount of Money that will need to be borrowed from the bank

=$2611374.46



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Task 7


PV =

PMT 1

1+ i( )

n

i

2611374.46 =

PMT 1 1+0.07

12

25*12

0.07

12

2611374.46 =

PMT 1 1+ 0.0058( )300

0.0058

2611374.46 =PMT 1 0.1747[ ]

0.0058

2611374.46 =PMT 0.8253[ ]

0.0058

2611374.46 = PMT 141.4869[ ]

PMT =

2611374.46

141.4869

PMT = 18456.6515

PMT 18456.65 The monthly repayment would be $18456.65


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Part BProblem 1


PV =

PMT 1 1+ i( )n i

2611374.46 =

PMT 1 1+0.09

12

20*12

0.09

12

2611374.46 =PMT 1 1+ 0.0075( )

240

0.0075

2611374.46 =PMT 1 0.1664[ ]

0.0075

2611374.46 =PMT 0.8336[ ]

0.0075

2611374.46 = PMT 111.145[ ]

PMT =2611374.46

111.145

PMT = 23495.2138

PMT 23495.21 The reason that there is a diffrence in the repayment amountis because the principal is being paid back 5 years earlier and the

interest rate has risen from 7% to 9%. By raising the interest rate

and lowering the peroid over which the loan is repayed, this has

caused the monthly payment to be increased. By going to a shorter

peroid and a higher interest rate you will end up paying $101855.871

more than if you used the lower interest rate and the longer peroid.


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Problem 2


Repayments per $1000 = PV =PMT 1 1+ i( )

n i

1000 =

PMT 1 1+0.07

12

25*12

0.07

12

1000 =PMT 1 1+ 0.0058( )

300 0.0058

1000 =PMT 1 0.1747[ ]

0.0058

1000 =PMT 0.8253[ ]

0.0058

1000 = PMT 141.4869[ ]

PMT =1000

141.4869

PMT = 7.067792142

Mortgage Value as Thousands=2611374.46

1000

=2611.37446

Repayments a Month = 2611.37446 7.067792142

= 18456.65189Recomended Monthly Income =18456.65189 4

=73826.6755

73826.68Recomended Yearly Income =73826.6755 12

=885920.106

885920.11 It is recomended that 25% of your income is needed it service loans. From this the

minimum level of income to comfortably service the loand can be calculated at

$885920.11 after tax.

The following Question has been answered

assuming that the deposit has been paid

and deducted from the loan amount.

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34413697 12 Mathematics a Applied Geometry Financial Maths