Activity 2: Nik's car loan (Maths)
1. PLAY the video segment
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In the video, Nik explains to Sophie and Tye that the car he bought was repossessed as the previous owner had money owing on it. |
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When Nik bought his gold station wagon the agreed price was $3500. He paid a $500 deposit and had to borrow the remaining $3000. Nik compared loans and chose a loan from a credit union. The interest rate was 12% and Nik agreed to make monthly payments over 2 years.
2. ANSWER the following questions:
a. How many monthly payments does Nik have to make over the loan?
To work out what Nik's monthly repayments would be, we can use the following formula (present value formula for an annuity):
M = repayment amount
N = the amount borrowed
r = the interest rate per payment (per month)
n = the number of repayments
So, using the details of Nik's loan:
N (the amount borrowed) = 3000
r (interest rate) = 12% pa = 0.12 pa = 0.01 per month
n (number of repayments) = 24
b. What would be the total amount paid for the car over the term of the loan? (Mn)
c. What is the total interest Nik would pay on the loan? (Mn-N)
3. Now use the same formula to determine the repayment amount (M) when a person borrows $2000 and repays it by 4 equal monthly instalments. The interest rate is 24% reducible, calculated on monthly balances.
This activity can be found in the NSW Money Stuff Teacher resource book– Mathematics page 36.
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
Rounds numbers appropriately to a desired degree of accuracy.
Understands and uses different representations of numbers including fractions, decimals, percentages and words.
General Mathematics (Stage 6)
Integrates mathematical knowledge and skills from different content areas in exploring new 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.