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Learning Sequence

Activity 4: Sophie's flat (Maths)

Sophie and her sister Nina are thinking of buying a flat together.

Before they go flat hunting, Sophie and Nina's parents help them to prepare a budget. Together they decide to estimate the cost of buying a flat.

If the purchase price of the flat is $100 000, Sophie would also have to pay stamp duty and legal fees which amount to about 10% of the price.

10% of $100 000 = $10 000

So, the total amount the sisters need would be about $110 000. They will need to pay a deposit of about 10% of the purchase price (the more the better) and between them they have saved
$10 000 for the deposit.

The loan required for the flat would be $100 000 ($90 000 for the balance of the purchase price and $10 000 for the stamp duty and legal fees).

Sophie and Nina need to know what their repayments would be each month, so they know whether they can afford to buy the flat. They work out what their repayments would be each month if the loan period was 25 years and the interest rate was 8%.

2. The sisters would need to pay $771.82 each month. How much is this each per week? Though each payment is equal, the division between principal and interest varies with each payment. On her computer, Sophie decides to set up a spreadsheet to understand her loan better. Set up her spreadsheet on your own computer entering Sophie's loan details and the formulas given below.

The first few lines of the spreadsheet will look like this:

3. USE  the complete table from your spreadsheet of Sophie's loan to answer these questions:

a. What was the interest paid for the:

• 1st time period?
• 14th time period?
• 30th time period?

How much of the principal has been paid after 5 years?

4. Many websites have loan calculators on them. To look at some of these SEARCH for 'loan calculators'. WRITE the names and URLs of 3 sites with loan calculators.

5. USE these calculators to find out:

a. How much would Sophie and Nina's monthly repayment be if the loan period was 20 years?
b. How much would the monthly repayments be over 25 years if the interest rate rose to 11%?
c. How much would the girls need to pay each month for a loan of $80 000 over 25 years at 8%?

This activity can be found in the NSW Money Stuff Teacher resource book– Mathematics page 37 .

Explore additional learning activities (which include extension and revision tasks) in the print resources section under Print resources - Victoria.

Linked Learning Outcomes - NSW
Theme 6: Mathematics in the Community
Learning Outcomes:
The student rounds numbers appropriately to a desired degree of accuracy.

General Mathematics (Stage 6)
Learning Outcomes
A student integrates mathematical knowledge and skills from different content areas in exploring new situations.
A student interprets the results of measurements and calculates and makes judgements about reasonableness.
A student makes informed decisions about financial situations.

Learning Outcomes – Victoria
Victorian Essential Learning Standards (VELS) Discipline-based learning
Domain: Maths
Dimension: Number, Space, Measurement, Chance and data, Structure and Working Mathematically
Level 5
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.
Students formulate conjectures and follow simple mathematical deductions.
Level 6
Students carry out arithmetic computations involving natural numbers, integers and finite decimals using mental and/or written algorithms.
Students choose, use and develop mathematical models and procedures to investigate and solve problems set in a wide range of practical, theoretical and historical contexts.

Learning Outcomes - Western Australia
(Maths)
A 18.8 Combines facility with symbolic representation and understanding of algebraic concepts to represent and explain mathematical situations.
A 19.6 Generates linear equations and inequalities that represent one and two constraints in a situation.