12 General Unit 4 Topic 1 (Part 1) 2020

Q.Which one of the following recurrence relations defines the sequence with starting value 4 and the rule ‘multiply by 3 and subtract 1’?

• A₀=1, An+1 = 3A_n - 4

• A₀=4, An+1 = 3A_n - 1

• A₀=3, An+1 = 4A_n - 1

• A₀=4, An+1 = A_n - 3

• A₀=1, An+1 = 4A_n - 3

Q.How many terms of the sequence defined by the recurrence relation A₀ = 25, An+1 = 2An − 30 are positive?

• 1

• 2

• 3

• 4

Q.The annual percentage rate of interest for a compound interest loan is 12.6% p.a., compounding monthly.

The balance of this loan after n months, An, can be modelled by the recurrence relation:

A₀ = 4000, A_n+1 = 1.0105A_n.

If the loan and interest is fully repaid after 5 months, how much in total will be paid?

• 4127.33

• 4170.66

• 4214.46

• 4258.71

• 4303.42

Q.A compound interest investment of principal $12 000 will earn interest at the rate of 10.8% p.a., compounding every six months. Which one of the following is a recurrence relation model for A_n, the balance of the investment after n six-month periods?

• A₀ = 12000, A_n+1 = 1.054 x A_n

• A₀ = 12000, A_n+1 = 0.108 x A_n

• A₀ = 12000, A_n+1 = 0.018 x A_n

• A₀ = 12000, A_n+1 = 1.018 x A_n

• A₀ = 12000, A_n+1 = 0.054 x A_n

Q.An investment of $50 000 is made at a fixed rate of interest compounding annually over a number of years. Which graph best represents the value of the investment at the end of each year?

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Q.A compound interest investment earns interest that compounds monthly. The balance of this investment after n months, An, can be found using the recurrence relation: A₀ = 15 000, A_n+1 = 1.0024 × A_n.

The balance of the investment can also be found using the rule:

• 1.0024 × (15 000)ⁿ

• 15000 × (1.24)ⁿ

• 1.0024 × (2.88)ⁿ

• 15000 × (1.0024)ⁿ

Q.A principal of $2000 is invested and will earn compound interest at the rate of 5.4% p.a., compounding quarterly. The effective annual rate of interest for this

investment is closest to:

• 5.2%

• 5.3%

• 5.4%

• 5.5%

Q.A compound interest investment earns interest at the rate of 3.6% p.a., compounding quarterly. If the balance after 4 years is $10 964.33, the principal investment amount is closest to:

• $6200

• $9500

• $10400

• $10600

Q.A compound interest investment of $10 000 earns $590.69 interest over a period of 15 months. If interest compounds monthly, the annual percentage rate of interest is

closest to:

• 1.5%

• 3.8%

• 4.6%

• 7.3%

Q. A reducing-balance loan is modelled by the recurrence relation shown below.

A₀ = 25 000, A_n+1 = 1.007 × A_n − 400

where An is the balance of the loan after n months.

The balance of the loan after five months is:

• $23 626.15

• $23 859.14

• $24 090.51

• $25 707.38