Recursion & Financial Maths Revision Quiz

The recurrence relation with starting value 6 and rule ‘multiply by 0.5 and add 4’ is:

• V₀ = 6, Vₙ₊₁ = 4Vₙ + 0.5

• V₀ = 6, Vₙ₊₁ = 0.5Vₙ - 4

• V₀ = 4, Vₙ₊₁ = 0.5Vₙ + 6

• V₀ = 6, Vₙ₊₁ = 0.5Vₙ + 4

• V₀ = 4, Vₙ₊₁ = 0.5Vₙ - 6

A sequence is generated by the recurrence relation V₀ = 50, Vₙ₊₁ = 0.84Vₙ + 15. After five steps, the value of the term, correct to two decimal places, is:

• 62.82

• 71.97

• 75.45

• 78.38

• 80.84

A recurrence relation that generates a sequence that grows only geometrically is:

• A₀ = 4, Aₙ₊₁ = 0.93Aₙ + 5

• A₀ = 5, Aₙ₊₁ = 1.05Aₙ

• A₀ = 6, Aₙ₊₁ = 0.94Aₙ

• A₀ = 7, Aₙ₊₁ = Aₙ

• A₀ = 10, Aₙ₊₁ = 1.04Aₙ - 2

The recurrence relation V₀ = 20000, Vₙ₊₁ = 1.045Vₙ + 200 could model a:

• compound interest loan with annual interest rate of 4.5% and annual payments of $200

• compound interest investment with annual interest rate of 4.5% and annual additions of $200

• reducing-balance depreciation at an annual rate of 4.5%

• compound interest investment with annual interest rate of 5.4% and monthly additions of $200

• compound interest loan with annual interest rate of 5.4% and monthly repayments of $200

The recurrence relation V₀ = 150000, Vₙ₊₁ = 1.0017Vₙ - 1800, is used to calculate the value of a reducing balance loan with fortnightly payments. The annual interest rate is closest to:

• 2.04%

• 3.85%

• 4.4%

• 6.8%

• 8.3%

A car is depreciated using a reducing-balance depreciation method, at the rate of 4.5% of its value each year. It was purchased for $24,990. A rule to calculate the value of the car after n years, V_n, is:

• V_n = 1.045ⁿ × 24990

• V_n = 1.00375ⁿ × 24990

• V_n = 0.956ⁿ × 24990

• V_n = 0.955ⁿ × 24990

• V_n = 0.045ⁿ × 24990

A company purchased a machine for $5000 and depreciates its value at a rate of 15% of its purchase price per year. When the book value falls below $1500 the company will write it off. The length of time that the machine will be in use is closest to:

• 2 years

• 3 years

• 4 years

• 5 years

• 6 years

A printing machine is bought for $20,000. Using flat rate depreciation, its value after 5 years will be $4000. Which of the following graphs best represents the value of the machine at the end of each year for this 5 year period?

• Graph A

• Graph B

• Graph C

• Graph D

• Graph E

Three thousand dollars is placed in an investment account compounding monthly at an interest rate of 6% per annum. The value of the investment in dollars, after n years, is given by:

• 1.005ⁿ × 3000

• 1.005¹²ⁿ × 3000

• 1.06ⁿ × 3000

• 1.06¹²ⁿ × 3000

• 0.06ⁿ × 3000

Robyn takes out a loan of $100 000 at an interest rate of 6.25% per annum compounded monthly. She makes payments of only the interest each month. How much money does she owe after 2 years?

• $106,250

• $100,000

• $112,500

• $87,500

• Not enough information to calculate