Maths Past Paper PDF

1\. WE1 Calculate the simple interest payable on a loan of \$8000 at 6% p.a. for 5 years. 2. Calculate the simple interest on each of the following loans. a. \$5000 at 9% p.a. for 4 years. b. \$4000 at 7.5% p.a. for 3 years. \$12 000 at 6.4% p.a. for 21 2 c. years. \$6000 at 8% p.a. for 11 2 d. year...

1\. WE1 Calculate the simple interest payable on a loan of \$8000 at 6% p.a. for 5 years. 2. Calculate the simple interest on each of the following loans. a. \$5000 at 9% p.a. for 4 years. b. \$4000 at 7.5% p.a. for 3 years. \$12 000 at 6.4% p.a. for 21 2 c. years. \$6000 at 8% p.a. for 11 2 d. years. 3. Calculate the simple interest on each of the following investments. a. \$50 000 at 6% p.a. for 6 months. b. \$12 500 at 12% p.a. for 1 month. c. \$7500 at 15% p.a. for 3 months. 5. WE2 The ticketed price of a mobile phone is \$800. Elena decides to purchase the phone using her credit card. After 1 month the credit card company charges interest at a rate of 15% p.a. Calculate the amount of interest that Elena must pay on her credit card after 1 month. 6. Arup decides to purchase a new sound system using her credit card. The ticketed price of the sound system is \$900. When Arup's credit card statement arrives, it shows that she will pay no interest if she pays the full amount by the due date. 7. Carly has an outstanding balance of \$3000 on her credit card for June and is charged interest at a rate of 21% p.a. a. Calculate the amount of interest that Carly is charged for June. b. Carly makes the minimum repayment of \$150 and makes no other purchases using the credit card in the next month. Calculate the amount of interest that Carly will be charged for July. c. If Carly had made a repayment of \$1000 at the end of June instead of \$150, calculate the amount of interest that Carly would then have been charged for July. d. How much would Carly save in July had she made the higher repayment at the end of June? 2. Compare the following two investments where simple interest is paid. Rate Principal Time Interest Investment A rA \$8000 4 years SIA Investment B rB \$7000 5 years SIB It is known that rA ∶ rB = 2 ∶ 3 and that investment B earned \$2000 more interest than investment A. Determine the values of rA, rB, SIA and SIB. Give your answers correct to 2 decimal places. (Use unrounded calculations to determine subsequent values.) Calculate the total cost of a \$3000 purchase given the terms described below. a. i. 12% deposit and monthly payments of \$60 over 5 years. ii. 20% deposit and weekly payments of \$20 over 3 years. iii. 15% deposit and annual payments of \$700 over 5 years. b. Which of these options is the best deal for a purchaser? 2. Calculate the amount of each repayment for a \$5000 purchase given the terms described below. a. 10% deposit with the balance plus simple interest paid monthly at 15% p.a. over 5 years. b. 10% deposit with the balance plus simple interest paid fortnightly at 12% p.a. over 5 years. c. 20% deposit with the balance plus simple interest paid monthly at 10% p.a. over 3 years. 3. Calculate the total repayment and the amount of each monthly repayment for each of the following loans. a. \$10 000 at 9% p.a. repaid over 4 years. b. \$25 000 at 12% p.a. repaid over 5 years. c. \$4500 at 7.5% p.a. repaid over 18 months. d. \$50 000 at 6% p.a. repaid over 10 years. e. \$200 000 at 7.2% p.a. repaid over 20 years. 8. WE4 A used car has a purchase price of \$9500. Dayna buys the car on the following terms: 25% deposit with balance plus interest paid at 12% p.a. over 3 years. a. Calculate the amount of the deposit. b. What is the balance owing? c. Calculate the interest payable. d. What is the total amount to be repaid? e. Determine the amount of each monthly repayment. 9. A department store offers the following terms: one-third deposit with the balance plus interest paid in equal, monthly instalments over 18 months. The interest rate charged is 9% p.a. Ming buys a lounge suite with a ticketed price of \$6000. a. Calculate the amount of the deposit. b. What is the balance owing? c. Calculate the interest payable. d. What is the total amount to be repaid? e. Determine the amount of each monthly repayment. Use the formula FV = PV(1 + r) n to calculate the amount to which each of the following investments will grow with interest compounded annually. a. \$3000 at 4% p.a. for 2 years. b. \$9000 at 5% p.a. for 4 years. c. \$16 000 at 9% p.a. for 5 years. d. \$12 500 at 5.5% p.a. for 3 years. e. \$9750 at 7.25% p.a. for 6 years. f. \$100 000 at 3.75% p.a. for 7 years. 2. Calculate the compounded value of each of the following investments. a. \$870 for 2 years at 3.50% p.a. with interest compounded 6-monthly. b. \$9500 for 21 2 years at 4.6% p.a. with interest compounded quarterly. c. \$148 000 for 31 2 years at 9.2% p.a. with interest compounded 6-monthly. d. \$16 000 for 6 years at 8% p.a. with interest compounded monthly. e. \$130 000 for 25 years at 12.95% p.a. with interest compounded quarterly. 3. WE5 Danielle invests \$6000 at 10% p.a. for 4 years with interest paid at the end of each year. Calculate the compounded value of the investment by calculating the simple interest on each year separately. 4. Ben is to invest \$13 000 for 3 years at 8% p.a. with interest paid annually. Determine the amount of interest earned by calculating the simple interest for each year separately. Year 1 2 3 Total Simple Interest 5. WE6 Simon has \$2000 to invest. He invests the money at 6% p.a. for 6 years with interest compounded annually. a. Use the formula FV = PV(1 + r) n to calculate the amount to which this investment will grow. b. Calculate the compound interest earned on the investment. 6. WE7 Calculate the future value of an investment of \$14 000 at 7% p.a. for 3 years with interest compounded quarterly. 16. Jasmine invests \$6000 for 4 years at 8% p.a. simple interest. David also invests \$6000 for 4 years, but his interest rate is 7.6% p.a. with interest compounded quarterly. a. Calculate the value of Jasmine's investment on maturity. b. Show that the compounded value of David's investment is greater than Jasmine's investment. c. Explain why David's investment is worth more than Jasmine's investment despite receiving a lower rate of interest. 17. Quan has \$20 000 to invest over the next 3 years. He has the choice of investing his money at 6.25% p.a. simple interest or 6% p.a. compound interest. a. Calculate the amount of interest that Quan will earn if he selects the simple interest option. b. Calculate the amount of interest that Quan will earn if the interest is compounded: i. annually ii. 6-monthly iii. quarterly. c. Clearly, Quan's decision will depend on the compounding period. Under what conditions should Quan accept the lower interest rate on the compound interest investment? d. Consider an investment of \$10 000 at 8% p.a. simple interest over 5 years. Use a trial-and-error method to determine an equivalent rate of compound interest over the same period. e. Will this equivalent rate be the same if we change: i. the amount of the investment ii. the period of the investment? 18. A building society advertises investment accounts at the following rates. Account 1: 3.875% p.a. compounding daily Account 2: 3.895% p.a. compounding monthly Account 3: 3.9% p.a. compounding quarterly Peter thinks the first account is the best one because the interest is calculated more frequently. Paul thinks the last account is the best one because it has the highest interest rate. Explain whether either is correct. 19. Two banks offer the following investment packages. Bankwest: 7.5% p.a. compounded annually, fixed for 7 years. Bankeast: 5.8% p.a. compounded annually, fixed for 9 years. a. Which bank's package will yield the greater interest? b. If a customer invests \$20 000 with Bankwest, how much would she have to invest with Bankeast to produce the same amount as Bankwest at the end of the investment period? 1. Calculate the depreciated value of an item for the initial values, depreciation rates and times given below. a. Initial value of \$30 000 depreciating at 16% p.a. over 4 years. b. Initial value of \$5 000 depreciating at 10.5% p.a. over 3 years. c. Initial value of \$12 500 depreciating at 12% p.a. over 5 years. 2. WE8 A laundromat installs washing machines and clothes dryers to the value of \$54 000. If the value of the equipment depreciates at a rate of 20% p.a., calculate the value of the equipment after 5 years. 3. A drycleaner purchases a new machine for \$38 400. The machine depreciates at 16% p.a. a. Calculate the value of the machine after 4 years. b. Calculate the amount by which the machine has depreciated over this period of time. 4. A tradesman values his new tools at \$10 200. For tax purposes, their value depreciates at a rate of 15% p.a. a. Calculate the value of the tools after 6 years. b. Calculate the amount by which the value of the tools has depreciated over these 6 years. c. Calculate the percentage of the initial value that the tools are worth after 6 years. 5. A taxi is purchased for \$52 500 with its value depreciating at 18% p.a. a. Determine the value of the taxi after 10 years. b. Calculate the accumulated depreciation over this period 14. A machine purchased for \$48 000 will have a value of \$3000 in 9 years. a. Use a trial-and-error method to determine the rate at which the machine is depreciating per annum. b. Consider the equation x = a n , a = √n x. Verify your answer to part a using this relationship. 15. Camera equipment purchased for \$150 000 will have a value of \$9000 in 5 years. a. Determine the rate of annual depreciation using trial and error first and then algebraically with the relationship 'if x = a n , then a = √n x '. b. Compare and contrast each method. 16. The value of a new tractor is \$175 000. The value of the tractor depreciates by 22.5% p.a. a. Determine the value of the tractor after 8 years. b. What percentage of its initial value is the tractor worth after 8 years? 17. Anthony has a home theatre valued at \$P. The value of the home theatre depreciates by r% annually over a period of 5 years. At the end of the 5 years, the value of the home theatre has been reduced by \$ P 12. Determine the value of r correct to 3 decimal places. 18. How and why is the formula for depreciation different to compound interest? y 1. Calculate the simple interest that is earned on \$5000 at 5% p.a. for 4 years. 2. MC Jim invests a sum of money at 9% p.a. Which one of the following statements is true? A. Simple interest will earn Jim more money than if compound interest is paid annually. B. Jim will earn more money if interest is compounded annually rather than monthly. C. Jim will earn more money if interest is compounded quarterly rather than 6-monthly. D. Jim will earn more money if interest is compounded annually rather than 6-monthly. 3. Benito has a credit card with an outstanding balance of \$3600. The interest rate charged on the loan is 18% p.a. Calculate the amount of interest that Benito will be charged on the credit card for the next month. 4. An LCD television has a cash price of \$5750. It can be purchased on terms of 20% deposit plus weekly repayments of \$42.75 for 3 years. Calculate the total cost of the television if it is purchased on terms. 5. Erin purchases a new entertainment unit that has a cash price of \$6400. Erin buys the unit on the following terms: 10% deposit with the balance plus interest to be repaid in equal monthly repayments over 4 years. The simple interest rate charged is 12% p.a. a. Calculate the amount of the deposit. b. Calculate the balance owing after the deposit has been paid. c. Calculate the interest that will be charged. d. What is the total amount that Erin has to repay? e. Calculate the amount of each monthly repayment. 6. A new car has a marked price of \$40 000. The car can be purchased on terms of 10% deposit and monthly repayments of \$1050 for 5 years. a. Determine the total cost of the car if it is purchased on terms. b. Calculate the amount of interest paid. c. Calculate the amount of interest paid per year. d. Calculate the interest rate charged. Understanding 7. Ryan invests \$12 500 for 3 years at 8% p.a. with interest paid annually. By calculating the amount of simple interest earned each year separately, determine the amount to which the investment will grow. 8. Calculate the compound interest earned on \$45 000 at 12% p.a. over 4 years if interest is compounded: a. annually b. 6-monthly c. quarterly d. monthly. 9. MC A new computer server costs \$7290. With 22% p.a. reducing-value depreciation, the server's value at the end of the third year will be closest to: A. \$1486 B. \$2257 C. \$2721 D. \$3460 10. MC An asset that was bought for \$34 100 has a value of \$13 430 after 5 years. The depreciation rate is closest to: A. 11% B. 17% C. 18% D. 21% 28 Jacaranda Maths Quest 10 Stage 5 NSW Syllabus Third Edition 11. The value of a new car depreciates by 15% p.a. Calculate the value of the car after 5 years if it was purchased for \$55 000. Communicating, reasoning and problem solving 12. Virgin Australia buys a new plane so that extra flights can be arranged between Sydney, Australia and Wellington, New Zealand. The plane costs \$1 200 000. It depreciates at a rate of 16.5% p.a. and is written off when its value falls below \$150 000. How long can Virgin Australia use this plane before it is written off? 13. Thomas went to an electronics store to buy a flat screen HD TV together with some accessories. The store offered him two different loans to buy the television and equipment. Loan 1: \$7000 for 3 years at 10.5% p.a. compounding yearly Loan 2: \$7000 for 5 years at 8% p.a. compounding yearly The following agreement was struck with the store. Thomas will not be penalised for paying off the loans early. Thomas does not have to pay the principal and interest until the end of the loan period. a. Explain which loan Thomas should choose if he decides to pay off the loan at the end of the first, second or third year. b. Explain which loan Thomas should choose for these two options. Paying off loan 1 at term. Paying off loan 2 at the end of 4 years. c. Thomas considers the option to pay off the loans at the end of their terms. Explain how you can determine the better option without further calculations. d. Why would Thomas decide to choose loan 2 instead of loan 1 (paying over its full term), even if it cost him more money? 14. Jan bought a computer for her business at a cost of \$2500. Her accountant told her that she was entitled to depreciate the cost of the computer over 5 years at 40% per year. a. How much was the computer worth at the end of the first year? b. By how much could Jan reduce her taxable income at the end of the first year? (The amount by which Jan can reduce her taxable income is equal to how much value the asset lost from one year to the next.) c. Explain whether the amount she can deduct from her taxable income will increase or decrease at the end of the second year.