Maths in Context Leaning Outcome 7 Commercial Mathematics Exercise Book (1-11) Page 1 of 7
Learning Outcome 7 Exercise 1 Complete the table below. Weekly earnings ($) 1. 500 Fortnightly earnings ($) Yearly (Annual) earnings ($) 2. 39 000 3. 2000 4. 760 5. 104 000 6. 1100 7. 3000 8. 2500 9. 100 000 Learning Outcome 7 Exercise 2 1. Harry is a part time attendant at the cricket ground. He gets paid $8.40 per hour for midweek games, and $10.60 for weekend games. Last week he worked the following hours: Thursday 3 h, Saturday 7.5 h, and Sunday 3.5 h. Calculate his total earnings for the week. 2. Ian works part-time at a petrol station on weekends. He gets $8.24 per hour on Saturday mornings, time-and-a-half on Saturday afternoons after 1 pm, and double-time on Sundays. Find how much Ian earned if he worked from 10 am to 5 pm on Saturday, and from 8 am to 1.30 pm on Sunday. 3. Calculate the rate of pay (to the nearest cent) for each of the following workers: (a) Jess earned $248.12 for 21 hours work (b) Kelly earned $61.73 for 7.5 hours work. 4. Leroy works as a veterinary assistant. He is paid $11.87 per hour for a standard 37.5 hour week, time-and-a-half on evenings and Saturdays, and double-time-and-a-half on Sundays. On a very busy week just after Christmas he worked a standard week plus 2 h on Thursday evening, 4 h on Saturday and 4h 30 min on Sunday. Calculate his total earnings for the week. Learning Outcome 7 Exercise 3 1. Nell has a casual job stapling together leaflets for a local politician. She is paid 85 cents per 100 leaflets completed. (a) How much would Nell earn for stapling 2000 leaflets? (b) How many leaflets would she need to staple in order to earn $72.25? (c) If it takes Nell 5 minutes to staple 100 leaflets, what would be her hourly rate of pay? 2. Olga has a job sewing shopping bags. She gets paid $2.40 for each bag completed. (a) How much will she earn for sewing 50 bags? (b) How many bags would she need to complete to earn $600? 3. Casual apple pickers are paid $4.82 for each box of apples picked. How many boxes would need to be picked for a worker to make $100? Page 2 of 7
Learning Outcome 7 Exercise 4 1. Steve s company pays commission only, at a rate of 18% on all sales. What would he earn if he made sales of: (a) $500 (b) $2000 (c) $5175 2. Terri works for a company that pays her a fixed wage of $160 per week, plus a commission of 4.5% on sales. What would she earn in one week if her sales were: (a) $500 (b) $2000 (c) $5175 (d) $20 000 3. Vaughn works as a sales representative for a farm chemicals company. He is paid a retainer of $800 per month, plus 9% commission on sales in excess of $10 000. Calculate Vaughn s monthly income on sales of: (a) $10 000 (b) $15 800 (c) $25 000 (d) $46 000 4. Wendy works as a real estate agent. She charges 5% of the first $25 000 of the selling price, and 2.5% on the remainder. Calculate the commission she receives on each of the following sales: (a) A block of land for $95 000 (b) A two-bedroom unit for $535 000 (c) A rural property for $4.2 million. Learning Outcome 7 Exercise 5 1. Carla normally earns $563 per week. She is about to take her four weeks annual leave. She is entitled to a holiday loading of 17.5% on four weeks annual leave. (a) Calculate the extra that she will receive as holiday loading (b) What will be her total pay for the four weeks of her holiday? 2. Dan is a nurse. His annual salary is $35 000. At the end of the year he is to get a 4% increase in pay. (a) How much extra will he earn per year? (b) What will be his new salary? (c) How much will he get paid each fortnight after the increase? 3. Emma s fortnightly pay recently increased from $628 to $682. (a) By how much did her pay increase? (b) What percentage increase in pay did she receive? Answer to one decimal place. [Hint: Percentage increase = Increase Original pay 100%] 4. Fred is to get a wage increase of 6.5%. His weekly wage now is $625. (a) What will be his weekly wage after the increase? (b) How much extra per year will Fred be paid? 5. After receiving a 5% wage increase, Greg now earns $682.50 per week. What was his wage before the increase? [Hint: $682.50 is 105% of the original wage. Use this fact to find 100% of the original wage] Page 3 of 7
Learning Outcome 7 Exercise 6 1. Find the take-home pay (net pay) for the following workers: (a) Gross pay is $412 per week, total deductions are $82.40 (b) Gross monthly pay is $2790, tax is $512 and other deductions are $105.76 (c) Gross pay is $1540 per fortnight, tax is $328, superannuation is $21.80 and union fees are $5.82 (d) Gross annual salary is $31 200, and monthly deductions are: tax $478.34; superannuation $37.60; other deductions $24.52. (Find net annual salary.) 2000/01 financial year income tax table Taxable Income Tax on this income $1-$6000 Nil $6001-$20 000 17 cents for each $1 over $6000 $20 001-$50 000 $2380 + 30 cents for each $1 over $20 000 $50 001-$60 000 $11 380 + 42 cents for each $1 over $50 000 $60 000 and above $15 580 + 47 cents for each $1 over $60 000 2. Calculate (i) the annual tax payable, and (ii) the net annual income, for workers who earn the following annual gross salaries. Use the 2001/01 tax table shown above. (a) $18 400 (b) $5200 (c) $26 900 (d) $74 500 (e) $51 000 3. Dara earns $1210 gross per fortnight. Calculate: (a) her gross annual salary (b) the annual amount of tax payable (c) her net fortnightly pay (to the nearest cent). 4. Larry s gross salary was $47 700. His employer deducted an amount of $412 from his pay each fortnight. (a) Calculate the total amount deducted for tax instalments. (b) Larry s work-related expenses totalled $2452. Calculate his taxable income. (c) Use the 2000/01 financial year income tax table in Question 2 above to calculate Larry s income tax. (d) Is Larry owed a refund or does he need to pay additional tax to the ATO? Calculate the amount involved. Learning Outcome 7 Exercise 7 1. Complete the following table: Original Price ($) Discount (%) Price after Discount ($) (a) $45.00 10 (b) $50.00 15 (c) $1.50 20 (d) $120.00 10 (e) $17.00 15 (f) $67.00 50 (g)$8.80 10 (h) $8.85 10 (i) $1480.00 15 (j) 148.00 15 Page 4 of 7
2. Calculate the percentage discount: Original Price ($) Discounted Price($) Percentage discount (%) (a) $60.00 $45.00 (b) $48.00 $24.00 (c) $84.00 $67.20 (d) $2650 $2252.50 (e) $8420 $5894 3. Calculate the original price: Discounted Price ($) Discount (%) Original Price ($) (a) $10.00 50 (b) $72.00 20 (c) $187.50 25 (d) $756 10 (e) $1960 30 Learning Outcome 7 Exercise 8 1. Calculate the GST and the price including GST for the following: Price before GST ($) 10% GST ($) Price including GST ($) (a) $45.00 (b) $50.00 (c) $1.50 (d) $120 (e) $17 (f) $67 (g) $8.80 (h) $8.85 (i) $1480 (j) $148 2. A restaurant menu gives the cost of a set meal as $60 plus GST. What will be the cost of the meal after adding 10% GST? 3. A ticket to a rugby game cost $55 before GST. (a) How much GST will be added? (b) What is the cost of the ticket after GST has been added? 4. A watch cost $231, including GST. What was the price of the watch before 10% GST was added? 5. A television cost $977.90, including 10% GST. How much GST was included in the price? Learning Outcome 7 Exercise 9 Use the simple interest formula I = PRT for questions 1 and 2. 1. Calculate the simple interest earned on an investment of $2000: (a) at an interest rate of 5% p.a., for 2 years (b) at an interest rate of 6.25% p.a., for 1 3 years (c) at an interest rate of 11.75% p.a., for half a year (d) at an interest rate of 4.2% p.a., for 3 months (e) at an interest rate of 5.5% p.a., for 1 month. 2 2. John borrowed $8000 from his credit union to buy a car. The interest on the loan is 11.5% p.a. (a) Calculate the interest charged for the year. (b) Calculate the total amount John owes the bank at the end of the year. Page 5 of 7
In questions 3 and 4 below, use the compound interest formula A = P(1 + r) n to calculate the accumulated amount (A) when a principal (P) is invested at r% (expressed as a decimal) for n time periods. 3. P = $2000, r = 12% p.a., n = 3 years, and the interest is: (a) compounded annually (b) compounded six-monthly (c) compounded quarterly (d) compounded monthly 4. Gemma won $10 000 in a competition. She decided to invest the money in an investment account for 5 years. She found out about the interest rates for three different types of accounts. Which of the three accounts is the best option for Gemma? Account A: interest rate 6% p.a., compounded monthly. Account B: interest rate 7.5% p.a., compounded annually. Account C: interest rate 6.75% p.a., compounded quarterly. Learning Outcome 7 Exercise 10 Use the depreciation formula V = (1 r) n to calculate the value of the item after n years, if the item depreciates at a rate of r% p.a. (r expressed as a decimal). Not all of the questions need the formula. 1. George s new computer cost $3890. If it depreciates by 20% each year, what will it be worth after 2 years? 2. Paula s new car cost $27 890. If it depreciates at a rate of 15% per year, how much will it be worth after: (a) 1 year (b) 4 years (c) 10 years? 3. John s new farm machinery cost $75 000. If it depreciates by 18% p.a., how much will it be worth after 3 years? 4. Judi s new car cost $43 500, and it depreciates by 20% in the first year. (a) What will it be worth after 1 year? (b) What will it be worth after 2 years if the depreciation rate during the second year is 15%? 5. If Katie bought a car for $40 000 and after one year it was worth only $32 800, what was the rate of depreciation? 6. Research depreciation rates on different types of cars by visiting the NRMA website http://www.nrma.com.au Learning Outcome 7 Exercise 11 1. The cash price of a car is $8500. The car dealer offers Peter the following terms: 20% cash deposit, followed by 24 monthly instalments of $330. (a) How much deposit must be paid? (b) What is the total amount that Peter will pay for the car if he buys it on terms? 2. The cash price for a computer is $2100. An advertisement states that the computer can be bought on terms of 15% deposit and $38 per week for one year. (a) How much is the deposit? (b) What is the total amount paid if the computer is bought on terms? 3. A motorbike costs $5750. Daniel has $750 and he is going to borrow the remainder. He agrees to pay the loan and interest in monthly instalments over 5 years at 11% p.a. flat rate of interest (flat rate means simple interest). (a) How much does Daniel borrow? (b) How much is the interest on the loan? (c) How much does Daniel owe altogether? (d) Calculate the monthly repayment (to the nearest cent). Page 6 of 7
4. Tom borrows $45 000 from the bank and agrees to repay the loan and interest in monthly instalments over 10 years at 11.5% flat rate of interest. (a) Calculate the amount of interest to be paid. (b) Calculate the total amount owing. (c) Calculate the monthly repayment. 5. Ann borrows $120 000 to buy a house. She can choose between several different monthly repayment plans as shown below: Period of loan Monthly instalment 5 years $2376 10 years $1393.20 15 years $1080 20 years $930 25 years $848.40 Calculate the total amount to be repaid under each option. 6. The initial costs involved in buying your own home can be quite high. Consider the following hypothetical example of costs involved when Jack and Jill bought a property for $185 000. Deposit: 10% of the purchase price Stamp duty on property: 2.7% of the purchase price Loan approval fee: $600 Stamp duty on loan: 0.4% of the loan amount Inspection and valuation fee: $475 Mortgage protection insurance: $921 Solicitor s fees: $1700. (a) Calculate the total amount they have to pay to cover all of these costs. (b) Calculate these initial costs as a percentage of the purchase price (nearest percent). This Concludes Learning Outcome 7 Make sure you have ticked each box in your online Exercise Summary Page Page 7 of 7