Recursion and Finance up to deprecetion (up to 3I)

Consider the recurrence relation below.

A₀ = 2, A_{n + 1} = 3 A_{n + 1}

The first four terms of this recurrence relation are

• 0,2,7,22 ....

• 1,2,7,22 ...

• 2,5,16, 49 ...

• 2,7,18,54 ...

• 2,7,22,67 ...

A printer was purchased for $680.

After four years the printer has a value of $125.

On average, 1920 pages were printed every year during those four years.

The value of the printer was depreciated using a unit cost method of depreciation.

The depreciation in the value of the printer, per page printed, is closest to

• 3 cents

• 4 cents

• 5 cents

• 6 cents

• 7 cents

The purchase price of a car was $26 000.

Using the reducing balance method, the value of the car is depreciated by 8% each year.

A recurrence relation that can be used to determine the value of the car after n years, C_n , is

• C₀ = 26 000,

  C_{n + 1} = 0.92 C_n

• C₀ = 26 000,

  C_{n + 1} = 1.08 C_n

• C₀ = 26 000,

  C_{n + 1} = C_n + 8

• C₀ = 26 000,

  C_{n + 1} = C_n - 8

• C₀ = 26 000,

  C_{n + 1} = 0.92 C_n - 8

• a piano depreciating at a flat rate of 6% per annum.

• a car depreciating with a reducing balance rate of 6% per annum.

• a compound interest investment earning interest at the rate of 6% per annum.

• a simpleinterest investment earning interest at the rate of 6% per annum.

The value of a compound interest investment, in dollars, after n years, Vn , can be modelled by the recurrence

relation shown below.

V₀ = 100 000, V_{n + 1} = 1.01 V_n

The interest rate, per annum, for this investment is

• 0.01%

• 0.101%

• 1%

• 1.01%

• 101%

Geoff purchased a computer for $4500. He will depreciate the value of his computer by a flat rate of 10% of

the purchase price per annum.

A recurrence relation that Geoff can use to determine the value of the computer after n years, V_n , is

• V₀ = 4500,

  V_{n + 1} = V_n – 450

• V₀ = 4500,

  V_{n + 1} = V_n + 450

• V₀ = 4500,

  V_{n + 1} = 0.9 V_n

• V₀ = 4500,

  V_{n + 1} = 1.1 V_n

• V₀ = 4500,

  V_{n + 1} = 0.1 (V_n -450)

• 660.00

• 670.00

• 672.80

• 678.40

• 685.60

A machine is purchased for $30 000.

It produces 24 000 items each year.

The value of the machine is depreciated using a unit cost method of depreciation.

After three years, the value of the machine is $18 480.

A rule for the value of the machine after n units are produced, V_n , is

• V_n = 0.872 n

• V_n = 24 000 n – 3840

• V_n = 30 000 – 24 000 n

• V_n = 30 000 – 0.872 n

• V_n = 30 000 – 0.16 n