12 General Unit 4 Topic 1 (part 2) 2020

Q.Julie has started a new job. She has a new superannuation account and her employer will deposit $850 each month into this account. Assume that the money in this account

will earn interest at the rate of 8.28% per annum, compounding monthly.

A recurrence relation model for the balance of this investment after n months, An, is

• A₀ = 0, A_n+1 = 1.0069 × A_n + 850

• A₀ = 0, A_n+1 = 1.069 × A_n + 850

• A₀ = 0, A_n+1 = 1.0828 × A_n + 850

• A₀ = 0, A_n+1 = 1.828 × A_n + 850

Q.An annuity is modelled by the recurrence relation shown below.

A₀ = 386 000, A_n+1 = 1.0065 × An − 5600

where A_n is the balance of the investment after n months.

The balance of the investment after four months is:

• $370 342.77

• $373 514.93

• $376 666.59

• $379 797.91

Q.An annuity is modelled by the recurrence relation shown below.
A0 = 386 000, An+1 = 1.0065 × An − 5600
where An is the balance of the investment after n months.
The annual percentage rate of interest for this investment is:
Hint: In recurrence relations formulas,   $r=1+\frac{i}{100}$  

• 1.5%

• 5.4%

• 6.5%

• 7.8%

Q.What is the principal amount for this annuity?

• $1653

• $3847

• $281 153

• $285 000

Q.What is the value of A, the balance of the annuity after payment 4?

Hint: Balance of loan ($) = Previous month’s balance – Principal reduction

• $261 626.25

• $267 891.94

• $269 477.61

• $269 500.19

Q.The interest charged on this annuity compounds monthly and monthly payments are received.

The annual percentage rate of interest for this annuity is closest to:

Hint: Interest Paid = Interest rate per payment period x the previous loan balance.

• 1.35%

• 5.08%

• 6.96%

• 16.12%

Q.Michelle will spend one year travelling the world. She invests $25 000 into an annuity that earns interest at the rate of 7.08% per annum, compounding monthly. Michelle

expects to receive exactly 12 regular monthly payments from this investment.

The monthly payment that Michelle receives is closest to:

Hint: Use present value annuity formula

• $1160

• $2160

• $3160

• $4160

Q.An annuity of principal $285 000 earns interest at the rate of 6.36% per annum, compounding monthly. Monthly payments of $3200 are received from this investment.

After how many payments will the balance of this investment first be below $270 000?

• 6

• 7

• 8

• 9

Q.A perpetuity will be set up to provide an annual prize of $400 to the best mathematics student in a school. Interest will be earned on the principal of the investment at a rate

of 3.4% per annum and will be used to pay for the prize every year. The amount that must be invested is closest to:

• $400

• $800

• $1176

• $11765

Q. A perpetuity has a balance of $120 000 after six years. Interest is earned at the percentage annual interest rate of 5% per annum. The perpetuity is used to provide an annual prize of value $6000.

After a further six years, what is the balance of the perpetuity?

• $84 000.00

• $86 654.33

• $120 000.00

• $123 563.76