Simple interest investments
$6000 at 5.8% p.a over 3 years
$1044
Calculate future value of a fixed-term investment of $4000 over 6 years at 7.5% p.a. interest compounding yearly.
$6173.21
A loaf of bread costs $2.85 today. The price increases at the same rate as inflation. The rate of inflation is 5%. Find the expected price of a loaf of bread after 2 years.
$3.14
New office carpets are purchased for $19 990. They depreciate in value at a rate of 28% per year. Calculate the salvage value of the carpets after 5 years.
$3867.90
What was the last country Miss Prater travelled to?
a) Tonga
b) England
c) Spain
d) New Zealand
d) New Zealand
$5600 at 13% p.a for 16 months
$970.67
a) Calculate future value of a fixed-term investment of $6453 over 3 years at 4.95% p.a. interest compounding yearly.
b) Find the total interest earned.
a) $7459.49
b) 1006.49
What is Miss Prater's favourite sport?
a) soccer
b) netball
c) oztag
d) cricket
a) soccer
Some office furniture depreciates in value from $44 900 to $32 440 in 2 years. Use the declining-balance formula to calculate the annual percentage rate of depreciation.
15%
Find the monthly repayment on $400 000 over 20 years.
$3471.28
When was Mr Martin born?
a) 1986
b) 1989
c) 1987
d) 1945
C - 1987
Use the compound interest formula to calculate the future value of a fixed-term investment of $950 over 3 years at 4.1% p.a. interest compounding quarterly.
$1073.67
In 3 successive years the annual rate of inflation was 2.8%, 3.5% and 4.1%. How much would you expect to pay at the end of these 3 years for a theatre ticket that cost $29.99 at the beginning of this period?
$33.22
Tai uses the declining balance method of depreciation to calculate tax deductions for her business. Tai’s computer is valued at $6500 at the start of the 2003 financial year. The rate of depreciation is 40% per annum.
a) Calculate the value of her tax deduction for the 2003 financial year. (1 mark)
b) What is the value of her computer at the start of the 2006 financial year? (2 marks)
a) Tax deduction = 40% x $6500 = $2600
b) Using S = V0(1-r)n
Value at the start of 2006 (n = 2006 - 2003 = 3)
= 6500(1-0.4)3
= $1404
Find the monthly repayment on $260 000 over 25 years, at 7.25% interest rate.
$1879.31
$3540 at 12.8% p.a. for 53 days
$65.80
What is Miss Prater's favourite takeaway?
a) Roll'd
b) GYG
c) KFC
d) Grill'd
b) GYG
Three years ago the price of chuck steak was $8.99/kg. It now costs $9.69/kg. Calculate the average yearly inflation rate, correct to two decimal places, that would produce this rise.
2.53%
A plasma TV depreciated in value by 15% per annum. Two years after it was purchased it had depreciated to a value of $2023, using the declining balance method. What was the purchase price of the plasma TV? (2 marks)
S = V0(1-r)n
2023 = V0(1-0.15)2
2023 = V0(0.85)2
V0 = 2023/(0.85)2
V0 = $2800
HSC 2024 Question 21 (3 marks)
William has a reducing balance loan on which he owes $5590. He makes monthly repayments of $110. The loan company charges interest at 24% per annum, compounded monthly. The spreadsheet shows some of the information for the next two months of the loan.
a) Complete the entries in the spreadsheet to show the balance owing on the loan at the end of two months.
b) Explain why the loan will never be repaid if William continues to make repayments of $110 per month.
a) $5593.64
b) Sample answer: Loan will never be repaid as the interest charged per month is more than the monthly repayment of $110. Answers could include: The balance owing on the loan is increasing.
Polly borrowed $11000. She repaid the loan in full at the end of two years with a lump sum of $12000. What annual simple interest rate was she charged?
Total interest paid = 12000 − 11000 = 1000
Using I = Prn
1000 = 11000 × r × 2
r = 1000/22000 = 0.04545 = 4.55 %
Calculate the amount that must be invested at 5% p.a. interest compounding annually to have $1600 at the end of 7 years.
$1137.09
HSC 2020 Question 21 (2 marks)
The inflation rate over the year from January 2019 to January 2020 was 2%. The cost of a school jumper in January 2020 was $122. Calculate the cost of the jumper in January 2019 assuming that the only change in the cost of the jumper was due to inflation.
122/(1+ 0.02) = $119.61
How old is Miss Prater?
21
HSC 2022 Question 36 (5 marks)
Frankie borrows $200 000 from a bank. The loan is to be repaid over 23 years at a rate of 7.2% per annum, compounded monthly. The repayments have been set at $1485 per month. The interest charged and the balance owing for the first three months of the loan are shown in the spreadsheet below.
a) What are the values of A and B? (2 marks)
b) After 50 months of repaying the loan, Frankie decides to make a lump sum payment of $40 000 and to continue making the monthly repayments of $1485. The loan will then be fully repaid after a further 146 monthly repayments. How much less will Frankie pay overall by making the lump sum payment? (3 marks)
a) r = 7.2% pa monthly
A = 199 715 × 0.006 = $1198.29
B = 199 428.29 + 1196.57 − 1485 = $199 139.86
b) Number of repayments = 50 + 146 = 196
Total amount repaid = 196 × $1485 + $40 000 = $331 060
Repayment under original conditions = 23 × 12 × $1485 = $409 860
Frankie saves = $409 860 − $331 060 = $78 800