ATAR Maths Applications Unit 4
Investigation – Reducing Balance Loans
Introduction
The aim of this investigation is to determine the specificalities and finances to buy three different cars,
based on offers made by three different banks. In order to achieve this, the basics of financial
mathematics including investing and borrowing needs to be utilised as well as the ability to analyse
certain situations.
Research
Cars
1. A small, fuel-efficient hatchback
o Model: Toyota Corolla
o Price: $28,981 brand new
o Reasons: excellent fuel efficiency, high performance, extra storage capacity
2. A 4WD for weekend adventures
o Model: Toyota Rav4
o Price: $38,664 brand new
o Reasons: ample cargo space, long list of safety technology and a user-friendly
infotainment system, great off-road capability
3. An environmentally friendly hybrid vehicle
o Model: Toyota Prius Prime
o Price: $34,100 used
o Reasons: high fuel efficiency, low emissions, boost in acceleration feel, and the added
benefit of EV Mode at full highway speed
Banks
1. ANZ: https://www.anz.com.au/personal/personal-loans/
2. NAB: https://www.nab.com.au/personal/personal-loans
3. Commonwealth Bank: https://www.commbank.com.au/personal-loans.html
Calculations
To begin with, all loans are taken out with a term of 5 years and are compounded monthly. Results are
shown on the next page.
, ATAR Maths Applications Unit 4
ANZ
Rate type: fixed rate
Establishment fees: $150
Loan services fees: $10/month
Late payment fee: $20
Toyota Corolla Toyota Rav4 Toyota Prius Prime
A loan of $29,000 is taken out A loan of $38,500 is taken out A loan of $34,000 is taken out
with ANZ to buy a Toyota with ANZ to buy a Toyota with ANZ to buy a Toyota Prius
Corolla Hatchback, with a term Rav4, with a term of 5 years at Prime, with a term of 5 years
of 5 years at 6.49% p.a. 6.49% p.a. compounded at 6.49% p.a. compounded
compounded monthly. monthly. monthly.
a) Monthly repayments a) Monthly repayments a) Monthly repayments
N = 5 x 12 N = 5 x 12 N = 5 x 12
I% = 6.49 I% = 6.49 I% = 6.49
PV = -29,000 PV = -38,500 PV = -34,000
PMT = ? PMT = ? PMT = ?
FV = 0 FV = 0 FV = 0
P/Y and C/Y = 12 P/Y and C/Y = 12 P/Y and C/Y = 12
∴ $567.28 will be paid a month ∴ $753.12 will be paid a month ∴ $665.10 will be paid a month
b) Total repayments b) Total repayments b) Total repayments
Total = pmts x compounds Total = pmts x compounds Total = pmts x compounds
total = 567.28(12 x 5) total = 753.12(12 x 5) total = 665.10(12 x 5)
total = $34,036 total = $45,187.20 total = $39,907.20
∴ $34,036 will be paid back ∴ $45,187.20 will be paid back ∴ $39,907.20 will be paid back
c) Interest charged c) Interest charged c) Interest charged
Interest = repayment – loan Interest = repayment – loan Interest = repayment – loan
= 34,036 – 29,000 = 45,187.20 – 38,500 = 39,907.20 – 34,000
= $5,036 = $6,687.20 = $5,907.20
∴ $5,036 in interest paid ∴ $6,687.20 in interest paid ∴ $5,907.20 in interest paid
d) Total cost of the loan d) Total cost of the loan d) Total cost of the loan
Total = total repayment + Total = total repayment + Total = total repayment +
establishment fee + loan establishment fee + loan establishment fee + loan
service fee service fee service fee
= 5,036 + 150 + 600 = 6,687.20 + 150 + 600 = 5,907.20 + 150 + 600
= $5,786 = $7,437.20 = $6,657.20
∴ $5,786 will be paid back ∴ $7,437.20 will be paid back ∴ $6,657.20 will be paid back
Investigation – Reducing Balance Loans
Introduction
The aim of this investigation is to determine the specificalities and finances to buy three different cars,
based on offers made by three different banks. In order to achieve this, the basics of financial
mathematics including investing and borrowing needs to be utilised as well as the ability to analyse
certain situations.
Research
Cars
1. A small, fuel-efficient hatchback
o Model: Toyota Corolla
o Price: $28,981 brand new
o Reasons: excellent fuel efficiency, high performance, extra storage capacity
2. A 4WD for weekend adventures
o Model: Toyota Rav4
o Price: $38,664 brand new
o Reasons: ample cargo space, long list of safety technology and a user-friendly
infotainment system, great off-road capability
3. An environmentally friendly hybrid vehicle
o Model: Toyota Prius Prime
o Price: $34,100 used
o Reasons: high fuel efficiency, low emissions, boost in acceleration feel, and the added
benefit of EV Mode at full highway speed
Banks
1. ANZ: https://www.anz.com.au/personal/personal-loans/
2. NAB: https://www.nab.com.au/personal/personal-loans
3. Commonwealth Bank: https://www.commbank.com.au/personal-loans.html
Calculations
To begin with, all loans are taken out with a term of 5 years and are compounded monthly. Results are
shown on the next page.
, ATAR Maths Applications Unit 4
ANZ
Rate type: fixed rate
Establishment fees: $150
Loan services fees: $10/month
Late payment fee: $20
Toyota Corolla Toyota Rav4 Toyota Prius Prime
A loan of $29,000 is taken out A loan of $38,500 is taken out A loan of $34,000 is taken out
with ANZ to buy a Toyota with ANZ to buy a Toyota with ANZ to buy a Toyota Prius
Corolla Hatchback, with a term Rav4, with a term of 5 years at Prime, with a term of 5 years
of 5 years at 6.49% p.a. 6.49% p.a. compounded at 6.49% p.a. compounded
compounded monthly. monthly. monthly.
a) Monthly repayments a) Monthly repayments a) Monthly repayments
N = 5 x 12 N = 5 x 12 N = 5 x 12
I% = 6.49 I% = 6.49 I% = 6.49
PV = -29,000 PV = -38,500 PV = -34,000
PMT = ? PMT = ? PMT = ?
FV = 0 FV = 0 FV = 0
P/Y and C/Y = 12 P/Y and C/Y = 12 P/Y and C/Y = 12
∴ $567.28 will be paid a month ∴ $753.12 will be paid a month ∴ $665.10 will be paid a month
b) Total repayments b) Total repayments b) Total repayments
Total = pmts x compounds Total = pmts x compounds Total = pmts x compounds
total = 567.28(12 x 5) total = 753.12(12 x 5) total = 665.10(12 x 5)
total = $34,036 total = $45,187.20 total = $39,907.20
∴ $34,036 will be paid back ∴ $45,187.20 will be paid back ∴ $39,907.20 will be paid back
c) Interest charged c) Interest charged c) Interest charged
Interest = repayment – loan Interest = repayment – loan Interest = repayment – loan
= 34,036 – 29,000 = 45,187.20 – 38,500 = 39,907.20 – 34,000
= $5,036 = $6,687.20 = $5,907.20
∴ $5,036 in interest paid ∴ $6,687.20 in interest paid ∴ $5,907.20 in interest paid
d) Total cost of the loan d) Total cost of the loan d) Total cost of the loan
Total = total repayment + Total = total repayment + Total = total repayment +
establishment fee + loan establishment fee + loan establishment fee + loan
service fee service fee service fee
= 5,036 + 150 + 600 = 6,687.20 + 150 + 600 = 5,907.20 + 150 + 600
= $5,786 = $7,437.20 = $6,657.20
∴ $5,786 will be paid back ∴ $7,437.20 will be paid back ∴ $6,657.20 will be paid back
