Worksheets12 General Unit 4 Topic 1 (part 2) 2020
Total questions: 10
Worksheet time: 29mins
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, An+1 = 1.0069 × An + 850
A0 = 0, An+1 = 1.069 × An + 850
A0 = 0, An+1 = 1.0828 × An + 850
A0 = 0, An+1 = 1.828 × An + 850
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 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+100i
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
