1. 1
   A savings account pays simple interest at a rate of 3% per year. Priya invests $2000 for 4 years and does not withdraw any money.

   (a)

   What is the total simple interest earned over the 4 years?

   [1 mark]

   • A$60
   • B$240
   • C$2240
   • D$24

   (b)

   What is Priya's total balance in the account at the end of the 4 years?

   [1 mark]

   • A$2060
   • B$2180
   • C$2240
   • D$2320

   (c)

   Priya is told that a rival bank instead offers 3% per year compound interest on the same $2000 deposit over the same 4 years. Which statement is correct?

   [1 mark]

   • AThe compound interest account gives exactly the same total interest as the simple interest account
   • BThe compound interest account gives less total interest than the simple interest account
   • CIt is impossible to compare the two accounts without knowing the currency
   • DThe compound interest account gives more total interest than the simple interest account

   Total for question 1: 3 marks

2. 2
   A car is bought for $18000. Its value depreciates by 12% each year.

   (a)

   Calculate the value of the car after 2 years, giving your answer to the nearest dollar.

   [2 marks]

   (b)

   Show that after 6 years the car's value has fallen by more than half of its original price.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Aisha deposits $5000 into a bank account that pays 2.5% compound interest per year. She leaves the money in the account, untouched, for 3 years.

   (a)

   Calculate the total amount in the account at the end of the 3 years, giving your answer to 2 decimal places.

   [3 marks]

   (b)

   Aisha's brother invests the same $5000 for 3 years in a different account offering simple interest at 3% per year. Determine, with justification, which account gives the greater total interest, and find the difference between the two amounts of interest.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   At the start of 2024, a town has a population of 42000. The population is growing at a rate of 1.8% per year.

   (a)

   Find the population of the town at the start of 2028, giving your answer to the nearest whole number.

   [4 marks]

   (b)

   The local council needs the population estimate to be within 50 people of the true value for planning purposes. Explain why rounding the annual growth rate to 1 significant figure (2%) before calculating the 2028 population would not be acceptable for this purpose.

   [4 marks]

   (c)

   A neighbouring town has a population of 38000 at the start of 2024 and is also growing at a constant percentage rate each year. By the start of 2027 (after 3 years of growth) its population has reached 41000. Find the annual percentage growth rate of this town, giving your answer to 1 decimal place, and state whether this town's growth rate is faster or slower than the town in part (a).

   [5 marks]

   Total for question 4: 13 marks

End of questions