CHAPTER REVIEW MULTIPLE CHOICE 1 Anthony earned $1016 in simple interest when he invested $19 800 for 9 months. The rate of simple interest was: A 5.13% B 6.14% C 6.84% D 7.62% E 8.21% 2 With an interest rate of 4.11% p.a., the sum of $634 was earned in simple interest over 2 1 years. The 2 amount invested was close to: A $6170 B $4892 C $7306 D $2937 E $5607 3 The Farmbrand dozen eggs (size 67) costs $2.40. With an inflation rate expected to average 3.5% over each of the next 4 years, the dozen eggs will then cost: A $2.50 B $2.60 C $2.70 D $2.75 E $2.80 4 An investment of $12 000 at 6.15% compounded quarterly to reach $15 000 will take close to: A 3 years B 4 years C 5 years D 6 years E 7 years 5 The points on the graph below show the balance of an investment at the start of each quarter for a period of six years. The same rate of interest applied for these six years. Balance (dollars) 0 1 2 3 Year 4 5 6 In relation to this investment, which one of the following statements is true? A Interest is compounding annually and is credited annually. B Interest is compounding annually and is credited quarterly. C Interest is compounding quarterly and is credited quarterly. D Simple interest is paid on the opening balance and is credited annually. E Simple interest is paid on the opening balance and is credited quarterly. EXAM TIP This question concerned the growth of an investment, but was formulated graphically rather than numerically. The aim was to test conceptual understanding of the different forms of investment growth. Only 37% of students were successful in answering this question. Teachers and students are reminded that graphical analysis of business and financial situations is a requirement of the study design. [ VCAA 2006] 6 A sum of $5000 is invested for 2 years at the rate of 4.75% p.a., compounded quarterly. The value of the interest at the end of the term, to the nearest dollar, is: A $495 B $5468 C $4532 D $936 E $391 7 A current household income is $61 800 p.a. and grows at the rate of 6% p.a. With this rate being constant, the number of years required for the household income to reach $100 000 is: A 7 B 8 C 9 D 10 E 11 Questions 8, 9 and 10 relate to the following. The table below shows the transactions in Anastasia s passbook for August. Date Transaction Deposits Withdrawals Balance 3 August 2009 Salary $1862.50 $2084.72 10 August 2009 $650.00 14 August 2009 Cheque 9652 $840.00 28 August 2009 Cheque 9654 $389.40 Financial arithmetic 445
8 In the bank statement above, the minimum balance for the month is: A $2084.72 B $1434.72 C $594.72 D $222.22 E $205.32 9 The interest earned on the minimum monthly balance if the bank pays 5.5% p.a. simple interest monthly is: A $9.55 B $6.58 C $2.73 D $1.02 E $0.94 10 The total debits for the month of August are: A $1490 B $1862.50 C $1879.40 D $1229.40 E $205.32 11 Ben has a store credit card with an outstanding balance of $850. If the interest rate is 24%, calculate the amount Ben will be charged if the balance is not paid by the due date. A $646 B $204 C $1054 D $826 E $25 12 An electrical store offers its customers an 8% discount if goods are fully paid for in cash on the camcorder with a marked price of $799 if she pays for it in cash? A $63.92 B $735.08 C $862.92 D $159.80 E $639.20 13 A hire-purchase agreement on a loan of $3000 requires 24 monthly payments. The effective annual rate interest is 17%. The interest paid, in dollars, is close to: A $289 B $361 C $482 D $679 E $531 14 A new cooktop worth $935 is bought under hire-purchase with a deposit of $100 and 18 monthly instalments of $50. The flat rate of interest is: A 8.94% B 7.69% C 6.34% D 5.19% E 4.88% 15 Brad investigated the cost of buying a $720 washing machine under a hire-purchase agreement. A deposit of $180 is required and the balance will be paid in 24 equal monthly repayments. A flat interest rate of 12% per annum applies to the balance. Brad correctly calculated the monthly repayment to be: A $22.50 B $25.20 C $26.10 D $27.90 E $29.70 EXAM TIP This question was based on a 2-year hire-purchase agreement. With a success rate of 36%, this question was not well done. However, another 30% of students started correctly, but only took into account 1 year s interest, not 2. [ VCAA 2007] 16 A laser printer is purchased for $790. It has an expected lifetime of 6 years and zero residual (scrap) value. The amount of depreciation to be allowed per year, in dollars, assuming a straightline depreciation, is: A $790 B $212 C $306.67 D $98.37 E $131.67 17 Equipment worth $18 600 is bought for a snowboard workshop. It depreciates at 12.5% p.a. constant depreciation. With zero scrap value, the book value of the equipment after 5 years is expected to be: A $11 625 B $6975 C $8114 D $5678 E $7316 18 A new computer costs $3490. If depreciation is calculated at 33% p.a. (reducing balance), then the computer s book value at the end of 5 years will be close to: A $471 B $509 C $432 D $567 E $288 19 A new kitchen in a restaurant cost $50 000. Its value is depreciated over time using the reducing balance method. The value of the kitchen in dollars 446 Maths Quest 11 Standard General Mathematics for the TI-Nspire
at the end of each year for 10 years is shown in the graph below. Value (dollars) 50000 40000 30000 20000 10000 0 1 2 3 4 5 6 7 8 9 10 Year Which one of the following statements is true? A The kitchen depreciates by $4000 annually. B At the end of five years, the kitchen s value is less than $20 000. C The reducing balance depreciation rate is less than 5% per annum. D The annual depreciation rate increases over time. E The amount of depreciation each year decreases over time. [ VCAA 2007] 20 A piece of equipment, originally worth $49 600, diminishes at a rate of 14.5% p.a. The owner decides to replace the equipment when its book value falls below $5000. The time passing before the next replacement is required is close to: A 10 years B 12 years C 14 years D 15 years E 16 years 21 The unit cost depreciation for a machine bought for $11 340 with scrap value of $750 and designed for 48 000 hours of operation is close to: A 6 c B 12 c C 22 c D 35 c E 49 c 22 A company car purchased for $28 500 and travelled 23 600 km in the first year and 20 400 km in the second year. In its third year, its book value will be: A $20 856 B $11 186 C $7644 D $9670 E $18 631 SHORT ANSWER 1 An investment in BT bonds of $18 000 over 3 1 2 years earned Rebecca the same amount as $21 600 invested at 7.5% in a term deposit for 5 years. Calculate the interest rate offered by BT bonds. 2 Find: a the simple interest on $2900 for 8 months at 5.85% p.a. b the annual rate of simple interest so that $1600 will amount to $2000 after 3 years c the number of years over which $5000 will amount to $6000 at 6.5% simple interest d the sum invested at 8% p.a. simple interest if it amounted to $4000 after 4 years. 3 Karen borrowed $1100 from a credit union at 8.55% per annum. She repaid the loan in a lump sum when the principal and interest amounted to $1400. How long, to the nearest year, did she keep the money? 4 Find each of the following and compare with the results from question 2. a The amount owing on $2900 for 8 months at 5.85% p.a. compounded daily. b The annual rate of compound interest so that $1600 will amount to $2000 after 3 years. c The number of years over which $5000 will amount to $6000 at 6.5% p.a. compounded quarterly. d The sum invested at 8% p.a. compound interest if it amounted to $4000 after 4 years. 5 It is estimated that inflation will average 2% per annum over the next 8 years. If a new machine costs $60 000 now, calculate the cost of a similar new machine in 8 years time, adjusted for inflation. Assume no other cost change. Write your answer correct to the nearest dollar. [ VCAA 2006] 6 The company prepares for this expenditure by establishing three different investments. a $7 000 is invested at a simple interest rate of 6.25% per annum for 8 years. Determine the total value of this investment at the end of 8 years. EXAM TIP showing the calculation but finding only the interest earned $3500. b $10 000 is invested at an interest rate of 6% per annum compounding quarterly for 8 years. Determine the total value of this investment at the end of 8 years. Write your answer correct to the nearest dollar. [ VCAA 2006] Financial arithmetic 447
7 For the given statement below, calculate: a the total credits b the total debits c the balance after each transaction d the final balance for the period of the statement. Date Transaction detail Debit Credit Balance 2 April 2009 Cheque 2694 $128.00 $5684.29 CR 5 April 2009 Salary $1693.80 11 April 2009 $800.00 19 April 2009 Salary $1693.80 23 April 2009 ABWDL Jam $800.00 Factory 29 April 2009 Cheque 2695 $2652.95 8 For the given statement in question 7, calculate the interest the account will earn in April if the bank pays 5 1 % p.a. simple interest 3 a on the minimum monthly balance b on the minimum daily balance. 10 Study the credit card statement below. 9 The minimum monthly repayment on a credit card is (a) 1.5% of the balance rounded down to the nearest dollar or (b) $25, whichever is greater. Calculate the minimum monthly repayment on a balance of: a $3500 b $1194.50 c $492.76 d $150 e $1820.53 Date Credit Debit Balance (amount owing) 1 January 2010 $1548.50 DR 8 January 2010 $500 Repayment 15 January 2010 $399 Purchase 1 February 2010??? Interest 8 February 2010??? Repayment??? Interest a If the interest rate is 16.5% p.a., calculate the daily rate of interest, correct to 4 decimal places (take 1 year 365 days). b Calculate the interest added to the account on 1 February. c On 8 February the minimum repayment of 5% is made. Calculate the amount of this repayment. d Calculate the outstanding balance on the year). 11 A new refrigerator is bought under a hire-purchase agreement for $3300 with $300 deposit and 24 monthly instalments of $153 each to be made. Calculate: a the amount of interest charged b the flat rate of interest c the effective rate of interest. 448 Maths Quest 11 Standard General Mathematics for the TI-Nspire
12 Alvin borrows $2000 from a bank at 14.6% p.a. calculated on a reducing monthly balance with monthly repayments of $40. a Calculate the amount still owed after the fourth repayment. b Calculate the amount of interest paid in 4 repayments. c Express the interest paid over the period of 4 months as a percentage of the total payments. 13 a scrap value of $1200 after 10 years. a Assuming straight-line depreciation, find the yearly depreciation change. b Find the amount by which depreciation at the end of the second year exceeds the depreciation at the end of the sixth year. 14 What was the original cost of an item that has a book value of $6344 after 7 years if the depreciation rate is 18% p.a.? 15 A photocopier is purchased for $11 400 and depreciates at an average rate of 2.1 10 3 cents per copy. a Calculate the book value of the photocopier after 4 10 8 copies were made. b After how many copies will the photocopier be written off (that is, have a zero scrap value)? EXTENDED RESPONSE 1 The passbook page below shows all the transactions for the month of February. Date Credit Debit Balance 2 Feb. $122.81 $877.35 7 Feb. $461.76 15 Feb. $931.99 21 Feb. $461.76 28 Feb. $819.89 a Calculate the balance after each transaction and enter the results in the table. b Calculate the total credits for the month of February. c Calculate the total debits for the month of February. d Find the interest that will be earned in February if the bank pays 5.25% p.a. simple interest on the minimum monthly balance. 2 1 to find the interest that will be earned in February if the bank pays 5.25% p.a. simple interest on the minimum daily balance. 3 An up to 55 days interest free period credit card was used for purchases which after the 30-day interval totalled $1825. Find the minimum amount payable, if the current credit limit on this card is $2000 and the bank requires the largest of $25 or 1.5% of the outstanding balance. Any excess above the card limit must also be included in the payment. 4 Chris bought an outboard motor for $5600 under hire purchase with $1000 deposit and 24 monthly instalments of $220. Calculate: a the amount of interest charged b the flat rate of interest c the effective rate of interest. 5 A personal loan of $4770, borrowed at 10% per annum reducing monthly balance, is to be repaid in monthly instalments of $80. Calculate the amount still owing at the end of the second month. 6 depreciation, find the yearly depreciation of the machinery. 7 A factory writes off 3.5% per annum for its building with the current book value of $450 000. If the adopted method to calculate depreciation is straight line, find the book value of the factory in 12 years time. Financial arithmetic 449
8 A road works company purchased machinery for $120 000. It depreciates at 10% per annum reducing balance. Calculate: a the book value of the machinery after 4 years b the total depreciation over the first 6 years c the number of years (to the nearest month) until the machinery has a value below $25 000 d the number of years (to the nearest month) until the machinery reaches its scrap value of $10 000 e a depreciation schedule for the first 5 years. 9 A company writes off 25% p.a. for reduced value depreciation of its machinery with a current book value of $90 000. Determine the purchase cost of the machinery 5 years ago. 10 A silver mining company purchased a new machine for $130 000. Calculate its book value after 5 years if it is 11 A machine cost $56 000 when new, and had an estimated trade-in value of $4000 and a useful life of 16 000 operating hours. Calculate: a the unit cost depreciation b the machine s book value after it has been operating for 7200 hours. 12 estimates that she needs to save $1400 over the next 12 months. She has already saved $1095 and is considering two options. Option A a Buying government bonds paying 9.85% p.a. i ii Option B b Opening a Super-Saver investment account that pays 9.55% p.a. compounded daily. i ii c Therefore, she saved some extra money and combined this with the total calculated in part b and reinvested for another 12 months at the same rate. How much does she need to add, to ensure that she has $1400 at the end of 12 months? 13 a a new mower for $4850. It depreciates at the rate of 18% of its value at the start of each year. i Find the value of the equipment at the end of 6 years, correct to the nearest dollar. ii Approximately how much time will pass before the equipment will be worth less than $500? b Ken decided to buy a new car, which cost $19 890. He traded in his old car and small trailer for $2600 as a deposit. The balance was to be paid on hire-purchase over 4 years, in weekly payments of $115. i How much will Ken pay over the period of 4 years? ii How much interest will Ken pay over that period? iii Calculate the flat rate of interest charged. iv Calculate the effective rate of interest. 14 Christopher wishes to purchase a notebook. Its retail value is $3599. Christopher s first option for financing the purchase is using a hire-purchase plan. The terms offered by the department store are 10% deposit with fortnightly instalments over 2 years at an interest rate of 9.2% p.a. a How much will Christopher need to withdraw from his savings account to pay the deposit? b Calculate the fortnightly repayments and total interest charge. 450 Maths Quest 11 Standard General Mathematics for the TI-Nspire
c What is the total cost of the notebook? A personal loan is advertised at 13.5% p.a. For Christopher to compare the interest rate, he needs to convert the hire-purchase flat rate of interest to the effective interest rate. d Calculate the effective interest rate and comment on how it compares with the personal loan rate. Another option is for Christopher to save up until he has the cash to pay for the notebook. He can place the balance of his savings account, $2268.50, into a term deposit offering 6.3% p.a. simple interest for a 2-year term. e Calculate the total value of his investment at the end of 2 years. f If he uses the term deposit investment towards the purchase of the notebook, what amount still needs to be paid? g What extra fortnightly savings will be needed over the next 2 years to make up the balance of $3599? h What is the main attraction of the hire-purchase option over the other two options? 15 Khan wants to buy some office furniture that is valued at $7000. a i A store requires 25% deposit. Calculate the deposit. The balance is to be paid in 24 equal monthly ii Determine the amount of each instalment. Write your answer in dollars and cents. b Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of $220. i Determine the total amount paid for the furniture at this store. ii Calculate the annual flat rate of interest charged by this store. Write your answer as a percentage correct to 1 decimal place. A third store has the office furniture marked at $7000 but will give 15% discount if payment is made in cash at the time of sale. c Calculate the cash price paid for the furniture after the discount is applied. Khan decides to extend his home office and borrows $30 000 for building costs. Interest is charged on the loan at a rate of 9% per annum compounding monthly. Assume Khan will pay only the interest on the loan at the end of each month. d Calculate the amount of interest he will pay each month. Khan paid $900 for a fax machine. This price includes 10% GST (goods and services tax). e Determine the price of the fax machine before GST was added. Write your answer correct to the nearest cent. f Khan will depreciate his $900 fax machine for taxation purposes. He considers two methods of depreciation. EXAM TIP This question was quite poorly answered and the deposit was often not allowed for. One mark was available for clearly identifying the interest of $1420 that was then to be used in the simple interest formula. EXAM TIP a period of time for this loan. A loan where the interest only is paid each month is not a reducing balance question as the balance does not decrease or increase. It becomes a simple interest calculation for one period (1 month in this case). EXAM TIP Reverse GST questions such as this continue to be a problem for many students. Answers of $818.20 were not accepted as accuracy correct to the nearest cent was required. Some students simply reduced $900 by 10% of $90 to get $810. Flat-rate depreciation i Calculate the annual depreciation in dollars. Financial arithmetic 451
Unit cost depreciation Suppose Khan sends 250 faxes a year. The $900 fax machine is depreciated by 46 cents for each fax it sends. ii Determine the value of the fax machine after 5 years. The books in Khan s office are valued at $10 000. g Calculate the value of these books after 5 years if they are depreciated by 12% per annum using the reducing balance method. Write your answer correct to the nearest dollar. Khan believes his books should be valued at $4000 after 5 years. h Determine the annual reducing balance depreciation rate that will produce this value. Write your answers as a percentage correct to 1 decimal place. [ VCAA 2007] ebookplus Digital doc Test Yourself 452 Maths Quest 11 Standard General Mathematics for the TI-Nspire