1. 1
   Ali invests money in a savings account and separately buys a car that depreciates in value, comparing compound growth and decay.

   (a)

   Ali invests 2000 dollars at $4\%$ compound interest per year. What is the value of his investment after 1 year?

   [1 mark]

   • A$2080$ dollars
   • B$2400$ dollars
   • C$2004$ dollars
   • D$2080.80$ dollars

   (b)

   Which multiplier represents a $4\%$ compound increase applied over 3 years?

   [1 mark]

   • A$1.04 \times 3$
   • B$1.12$
   • C$3 \times 1.04$
   • D$1.04^3$

   (c)

   Ali's car, worth 15000 dollars, depreciates at $10\%$ per year. What is the depreciation multiplier per year?

   [1 mark]

   • A$0.1$
   • B$1.1$
   • C$0.9$
   • D$0.09$

   Total for question 1: 3 marks

2. 2
   Priya is comparing two savings accounts with different compound interest rates over several years to decide where to invest her savings.

   (a)

   Priya invests 3500 dollars at a compound interest rate of $3.5\%$ per year. Calculate the value of her investment after 2 years, giving your answer to the nearest cent.

   [2 marks]

   (b)

   A second account offers $3\%$ per year compound interest but Priya invests for 3 years instead. Calculate the value of 3500 dollars invested at $3\%$ for 3 years, and state which account gives the higher return.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A logistics company is calculating the depreciation of a delivery van over several years and comparing it to the equivalent single annual depreciation rate.

   (a)

   A delivery van is bought for 28000 dollars and depreciates by $15\%$ in its first year and $12\%$ in its second year (each percentage applied to the value at the start of that year). Calculate the value of the van after 2 years, giving your answer to the nearest dollar.

   [3 marks]

   (b)

   Calculate the single annual percentage depreciation rate that would give the same overall reduction in value over the 2 years as in part (a), giving your answer to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A financial adviser is working backwards from a known compound interest outcome to find the annual interest rate, using logarithms or roots to solve the resulting equation.

   (a)

   An investor deposits 6000 dollars into an account paying $r\%$ compound interest per year. After 4 years the account is worth 7204.90 dollars. Using the formula $A = P\left(1 + \frac{r}{100}\right)^n$, set up an equation and find $\left(1 + \frac{r}{100}\right)^4$ as a decimal.

   [4 marks]

   (b)

   Using your answer to part (a), find the annual compound interest rate $r$, giving your answer to 1 decimal place.

   [4 marks]

   (c)

   The investor is offered an alternative: invest the same 6000 dollars in an asset that depreciates by $4.7\%$ per year for 4 years (the same rate as part (b), but as a decrease), then recovers with a one-off $30\%$ increase in year 5. Calculate the final value after 5 years, giving your answer to the nearest cent, and compare it with the 7204.90 dollars from the original compound interest account.

   [5 marks]

   Total for question 4: 13 marks

End of questions