General Maths compound interest recurrence relations part 1

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, A_n+1 = 3A_n − 4

• A₀ = ₄, A_n+1 = 3A_n − 1

• A₀ = 3, A_n+1 = 4A_n − 1

• A₀ = 4, A_n+1 = A_n − 3

• A₀ = 1, A_n+1 = 4A_n − 3

Which one of the following recurrence relations defines the sequence with starting value 1 and the rule ‘multiply by 4 and add 2’?

• A₀ = 1, A_n+1 = 4A_n + 2

• A₀ = 4, A_n+1 = A_n + 2

• A₀ = 1, A_n+1 = 2A_n + 4

• A₀ = 2, A_n+1 = 4A_n + 1

• A₀ = 2, A_n+1 = 4A_n + 2

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

• 1

• 2

• 3

• 4

• 5

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

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

A₀ = 3000, A_n+1 = 1.0097A_n

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

• $3029.10

• $3148.35

• $1890

• $3118.11

The annual percentage rate of interest for a compound interest loan of $4000 is 12.7% per annum, compounding fortnightly. What is the recurrence relation for this loan?

• A₀ = 4000, A_n+1 = 0.0049A_n

• A₀ = 4000, A_n+1 = 1.0049A_n

• A₀ = 4000, A_n+1 = 1.127A_n

• A₀ = 4000, A_n+1 = 1.4885A_n

A compound interest investment of principal $12 000 will earn interest at the rate of 10.8% per annum, 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 = 12 000, A_n+1 = 1.054A_n

• A₀ = 12 000, A_n+1 = 1.108A_n

• A₀ = 12 000, A_n+1 = 1.018A_n

• A₀ = 12 000, A_n+1 = 1.15A_n

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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David has some money to invest and would like to earn as much interest as possible in the first year of the investment. Which one of the following interest rates should he choose?

• 3.1% per annum, compounding monthly

• 3.2% per annum, compounding quarterly

• 3.2% per annum, compounding monthly

• 3.2% per annum, compounding annually

A principal of $2000 is invested and will earn compound interest at the rate of 5.4% per annum, compounding quarterly. The effective annual rate of interest for this investment is closest to:

• 5.6%

• 5.3%

• 5.4%

• 5.5%

Calculate the effective annual rate of interest for a loan of 12.5% per annum compounding quarterly. Round your answer to two decimal places.

• 13.10%

• 0.13%

• 1.97%

• 3.13%

• 13.75%