• Each part of this test has similar items that test a certain question type.
• Errors made will indicate areas of weakness.
• Each weakness should be treated by going back to the section listed.
These questions can be used to assess parts of outcomes NS5·1·2, NS5·2·2.
diagnostic test 4
1 a Find the simple interest charged on $600 at 12% pa for 5 years.
b What is the simple interest earned by $14 260 invested for 3 years at 4% pa?
c Find the interest charged on a loan of $85 000 taken over 15 years if a simple interest rate of 8% pa is charged.
2 a Find the simple interest charged on $860 at 6 % pa for 5 years.
b What interest would be paid on $25 000 invested for 6 years at a simple interest rate of 9·3% pa?
c Find the simple interest earned if $900 is invested for 3 years at a rate of 6 % pa.
3 a What is the simple interest on $2400 at 8% pa for 5 months?
b Find the simple interest on $900 for 240 days at a rate of 11% pa.
c What is the simple interest paid on $1950 invested for 7 months at 0·75% per month?
4 a Jodie borrowed $78 000 for 4 months at 12·75% pa simple interest to pay for her new house while her old one was being sold. How much interest did she pay?
b I paid $8000 to borrow $50 000 for 2 years. What was the rate of simple interest charged?
c Troy borrowed $1200 at 1·5% per month simple interest. Which is the best estimate of the interest charges for 6 months:
$20, $100, $200 or $1800?
5 a Find the compound interest earned if $9000 is invested for 3 years at 13% pa if interest is compounded yearly. Answer correct to the nearest cent.
b $12 000 is invested at a compound interest rate of 9% pa. Interest, however, is compounded monthly. Calculate the amount to which the investment will grow in 2 months.
c $12 500 is invested at a compound interest rate of 9% pa. Interest, however, is compounded monthly. Use the formula to calculate the amount to which the investment will grow in 4 years.
6 a A new computer depreciates by 30% per year. It costs $4000 new.
What will it be worth in 4 years?
b If the population of Bilby Downs is decreasing by 20% of its
population every year, what would be the population in 2 years if it is now 800?
c Carol paid $2200 for a new video unit. Use the depreciation formula to find the value of the unit in 6 years if its rate of depreciation is 25% pa.
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NEW SIGNPOST MATHEMATICS 10 STAGE 5.1–5.3
7 a Reducible interest at 6% pa is charged on a loan of $50 000. Annual repayments of $5000 are made. Calculate how much is still owing after
i 1 year ii 2 years iii 3 years
b A loan of $300 000 is charged 8% pa reducible interest. Quarterly payments of $9000 are made. Calculate the amount still owing after 1 year (ie, the first four quarterly payments).
8 a Use the table on page 120 to find approximate reducible interest rates equivalent to the following flat rates, if the loan is repaid in monthly instalments over 5 years.
i 6·69% pa flat ii 11·79% pa flat iii 3·76% pa flat
b Find the size of each monthly repayment (to the nearest dollar) on a loan of $35 800 taken at a rate of 9% pa reducible, over 20 years.
(Use the table on page 120.)
9 Use the table of repayments on page 126, to find the monthly repayments for the following loans.
a $30 000 taken over 15 years at 7% pa b $45 000 taken over 10 years at 6·5% pa c $75 000 taken over 25 years at 8·5% pa
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CHAPTER 4 CONSUMER ARITHMETIC
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Chapter 4 | Revision Assignment
1 Determine the amount of simple interest earned by the following:
a $1500 at 7% pa over 5 years b $950 at 9·5% pa over 3 years c $2200 at 8% pa over 6 months d $660 at 1·5% per month over
9 months
2 Bobby bought a video recorder which had a cash price of $850 by paying 10%
deposit and the balance over 2 years at a simple interest rate of 15% pa. Find:
a the deposit b the balance owing
c the amount of interest paid d the amount of each monthly
repayment
3 Kylie purchased a microwave oven by paying $45 deposit and 18 monthly instalments of $21.30.
a How much did she pay altogether for the oven?
b How much interest did she pay if the cash price was $365?
4 Kate’s savings account gives interest of 4% pa. Interest is calculated and added to her account every 6 months. If she starts with $2000 in the account and does not use the account for 2 years, what will her new balance be?
5 A loan is to be repaid, with interest, over a 3-year period. Which interest rate would produce the least amount of interest on the loan?
A 1·2% per month reducible interest B 1·2% per month simple (flat) interest C 12% per annum reducible interest D 12% per annum simple interest
6 $24 000 is invested for 2 years. Interest is paid at 14% pa and is compounded annually. Interest is not withdrawn. How much interest will have been earned after 2 years?
7 Machinery valued at $140 000 depreciates at a rate of 16% pa. Find the value of the machinery after 3 years.
8 A video recorder is purchased under the following terms.
a Find the total amount paid for the video recorder.
b If the marked price had been $800, what percentage are the additional charges of the marked price?
9 Use the table on page 120 to convert a reducible rate of 16% pa, with monthly repayments paid over 20 years, to a flat rate. Hence, find the size of each monthly repayment (to the nearest dollar) on a loan of $72 000 taken at a rate of 16% pa reducible over 20 years.
10 Jack decided to invest $5 at 13% pa compound interest for 200 years, with interest to be added annually. His nearest relative living after 200 years would inherit the proceeds.
a Find the amount the relative should inherit.
b Find the amount the relative should inherit if the interest rate had been 13% pa simple (flat) interest.
assignme
Repayments: $41.85 each month for 2 years.
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NEW SIGNPOST MATHEMATICS 10 STAGE 5.1–5.3Chapter 4 | Working Mathematically
1 Find the number of three-digit numbers possible if only the digits 0, 1, 2, 3, 4 and 5 may be used, the number must be a multiple of 5, and no digit may be used more than twice in the same number.
2 Of the 30 students in 10M, 13 love surfing, 15 love hiking and 7 love neither.
a How many students love both surfing and hiking?
b How many love surfing but not hiking?
c How many love hiking but not surfing?
3 A man and his granddaughter share the same birthday. For six consecutive birthdays the man’s age is an exact multiple of his granddaughter’s age. How old is each of them at the 6th of these birthdays? Can you find another set of numbers that work, but is highly unlikely?
4 Roger started a trip to the country between 8 am and 9 am when the hands of the clock were together. He arrived at his destination between 2 pm and 3 pm, when the hands of the clock were exactly 180°
apart. How long did he travel?
5 If 3! = 3 × 2 × 1 (pronounced 3 factorial), 5! = 5 × 4 × 3 × 2 × 1 and
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, how many zeros are there at the end of the answer to 20!? (A calculator will be of no help.)
6 a For Australia in 1999:
i How many people were killed on the road?
ii How many fatalities were there per 100 000 people?
iii Therefore, what is an estimation of Australia’s population according to these figures?
b Where did Australia rank among these 18 OECD countries in terms of least fatalities per 100 000 population?
c Compared to 1998, which country in 1999 had:
i the greatest decrease in fatalities?
ii the greatest increase in fatalities?
1 Compound interest
2 Who wants to be a millionaire?
1 Compound interest 2 Depreciation 3 Reducible interest nt
me gin ass
4B
Road safety comparisons:
fatalities OECD countries 1999 Number of fatalities in 1999
1999 %
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