Loan amortization schedule (Ques 3)

assignment_4

Question 1

The Sydney Harbour Bridge is a well known icon around the world.

The Sydney Opera House is about 500m away and from it, the angle of elevation

to the top of the bridge is measured as 14°54′ (to the nearest minute).

The place where this measurement is made is 1m above the

water level.

On the other side of the harbour bridge, a second reading is taken from the second floor of a building

700m away and 20m above the water level. The angle of elevation is observed to be 9°15′ (to the

nearest minute).

(a) Calculate an estimate of the height of the Harbour Bridge above the

water level.

(b) Discuss all possible errors in all measurements taken.

(c) Give a range for the maximum and minimum height.

Question 2

Three dice are thrown and the sum on the faces are recorded. This would

give values ranging from 3 (1-1-1) to 18 (6-6-6).

The experiment is run 300 times.

(a) Either carry out the experiment by rolling 3 dice, 300 times or use

Excel to simulate this experiment (Assistance is offered on how to do

this in a consultation session if required).

(b) Present the data in a table showing the frequency and cumulative

frequency columns.

(c) Compute the median, upper and lower quartiles

(d) Calculate the mean and standard deviation for the results of your

experiment either by the use of the stats mode on your calculcator

or using excel.

(e) Interprete the mean as an area and use Simpson’s Rule with 5 values,

to estimate the mean again, (using the median, the quartiles and the

upper and lower extremes of 3 and 18). Comment on how accurate

this is.

Question 3
People often are lost when it comes to knowing how much to

they can borrow to buy their homes.

Construct a simple spreadsheet application with the following

as input variables

The interest rate (% pa compounded monthly)

The amount to be borrowed.

The term in years of the loan.

The combined salary of the people buying the house.

The output of the calculator should include

(a) The monthly repayment for the loan.

(b) An estimate of when the loan would be half paid off.

(c) The percentage of the combined salary the repayment represents.

(d) The total interest paid out over the full term.

(e) The increase in repayment per month, should there be a 1% increase in interest rates.

(f) The decrease in the term if they switch to fortnightly repayments instead of monthly.

Present printouts for the following examples.

1. A couple on $150,000 wanting to borrow $500,000 over 30 years at 4.5% pa

2. A sole income earner on a salary of $80,000 wanting to borrow $200,000 over 25 years at 5% pa

3. A student earning $30,000 taking a share in a house requiring a loan (for his part) of $100,000

over 10 years at 6% pa.

Question 4
To make a rectangular grid of 2 rows of 3 squares requires 17 matches.

(a) How many matches would you need to make rectangular grids of m

rows of n squares?

(b) Write down a formula relating M, the number of matches

and n for an n x n square.

(c) Extend your analysis for the equilateral triangle .

(d) Extend your analysis for hexagons.

n = 2 n=2

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