Maths Questions "Recursion and Financial Modelling" 1.

Maths Questions "Recursion and Financial Modelling"

1.The amount of money in a bank account after n years, Vn, can be modelled by the recurrence relation

                       V0 = 12 000,                 Vn+1 = 0.92Vn

The amount of money is

Select one:

a. growing at the rate of 8% per annum

b. decaying at the rate of 9.2% per annum

c. decaying at the rate of 8% per annum

d. neither growing nor decaying

e. growing at the rate of 9.2% per annum

2. A musician purchased a new grand piano for $17 990. After 8 years it will have an estimated value of $12 500. If the value of the piano is depreciated using a reducing-balance method, the annual rate of depreciation, is closest to

Select one:

a. 30.5%

b. 4.45%

c. 69%

d. 4.66%

e. 43.9%

3. Alistair borrows $4500 from a bank and will pay interest at the rate of 3.6% per annum, compounding monthly.

    A recurrence relation that models the value of Alistair's loan after n months, Vn, is

Select one:

a. V0 = 4500,                    Vn+1 = 1.36Vn

b. V0 = 4500,                    Vn+1 = 1.003Vn

c. V0 = 4500,                    Vn+1 = 1.036Vn

d. V0 = 4500,                    Vn+1 = 1 + 3.6Vn

e. V0 = 4500,                    Vn+1 = (1 + 3.6)Vn

4. A sum of $3500 is invested in an account that pays 2.4% per annum simple interest.

A recurrence relation that models the value of the investment after n years, Vn, is

Select one:

a.V0 = 3500, Vn+1 = Vn + 24

b.V0 = 3500, Vn+1 = Vn - 84

c.V0 = 3500, Vn+1 = Vn + 84

d.V0 = 3500, Vn+1 = 2.4Vn

e.V0 = 3500, Vn+1 = Vn - 24

5. The graph below shows the depreciation in the value of a car over a period of 5 years. In the graph, Vn is the value of the car after n years. A rule for the value of the car after nyears is

Select one:

a.Vn = 35 000 – 5000n

b.Vn = 35 000n – 5000

c. Vn = 35 000 – n

d.Vn = 5000n – 35 000

e.Vn = 5000 – 35 000n