Chapter 8 Formative

A recurrence relation that generates the sequence 2, 7, 22, 67, 202, ... is

• T₀ = 2, Tₙ₊₁ = Tₙ + 5

• T₀ = 2, Tₙ₊₁ = 2Tₙ + 1

• T₀ = 2, Tₙ₊₁ = 3Tₙ + 1

• T₀ = 2, Tₙ₊₁ = 3.5Tₙ

The balance of a reducing-balance loan after n monthly payments can be modelled by the recurrence relation
V₀ = 12 000, Vₙ₊₁ = 1.0125Vₙ - 1300.
After five months, the balance of the loan is

• $3205

• $6104

• $7313

• $9070

The balance of a reducing-balance loan after n monthly payments can be modelled by the recurrence relation V₀ = 12 000, Vₙ₊₁ = 1.0125Vₙ - 1300 This loan has

• monthly interest rate 12.5% and monthly payments of $1300

• monthly interest rate 15% and monthly payments of $1300

• monthly interest rate 12.5% and yearly payments of $1300

• annual interest rate 15% and monthly payments of $1300

A reducing-balance loan of $8000 will be repaid with quarterly payments. The amortisation table for this loan is shown below:

The annual percentage interest rate on this loan is

• 1.2%

• 3.42%

• 3.5%

• 8.75%

Leasa borrows $150,000 to purchase a flat. She will pay interest at the rate of 6.25% per annum, compounding fortnightly and will make fortnightly payments so that the loan is fully repaid after 15 years.

Leasa’s fortnightly repayments will be closest to

• $593

• $900

• $1286

• $1308

The recurrence relation below is used to model a financial situation. V₀ = 24 000, Vₙ₊₁ = 1.0205Vₙ – 492 The financial situation could be

• an interest only loan of $24 000 at 8.2% per annum interest, compounding quarterly with quarterly payments of $492

• an annuity investment of $24 000 earning 8.2% per annum interest, compounding quarterly, with quarterly additions of $492

• an interest only loan of $24 000 at 2.05% per annum interest, compounding annually with annual payments of $492

• an annuity investment of $24 000 earning 8.2% per annum interest, compounding quarterly, with quarterly additions of $492

Carol invests $170 000 into an annuity which pays 7.2% compound interest per annum, compounding monthly.

Carol would like the investment to provide monthly payments for a period of five years. The monthly payment that Carol will receive is closest to

• $577

• $1020

• $2450

• $3382

Carol invests $170 000 into an annuity which pays 7.2% compound interest per annum,

compounding monthly.

If Carol receives monthly payments of $2500, the number of months that she will receive the full regular monthly payment is

• 86

• 87

• 88

• 119

Leigh borrows $35 000 to complete home renovations. Compound interest will be charged at the rate of 4.6% per annum, compounding monthly.

If Leigh makes monthly payments of $1529.24, the amount of interest he has paid after one year is closest to

• $1253

• $1610

• $16,649

• $17,098

Janet deposited $1200 into an investment fund every month for 20 years to save for her retirement. Throughout the 20-year period, the investment fund paid 5.35% per annum compound interest, compounding monthly.

When she retired, Janet purchased an annuity that pays 4.5% per annum compounding monthly, from which she receives a monthly payment for 20 more years.

The monthly payment that Janet receives, correct to the nearest cent, is

• $1956.80

• $2946.56

• $3164.50

• $3249.78