Financial Mathematics 3: Depreciation

Transcription

1 Finncil Mthemtics 3: Deprecition Student Book - Series M-1 25% p.. over 8 yers Mthletics Instnt Workooks Copyright

2 Finncil mthemtics 3: Deprecition Student Book - Series M Contents Topics Topic 1 - Modelling deprecition Topic 2 - Stright-line deprecition Topic 3 - Declining lnce method Topic 4 - Comprison of methods Topic 5 - Deprecition s tx deduction Dte completed Prctice Tests Topic 1 - Topic test A Topic 2 - Topic test B Author of The Topics nd Topic Tests: AS Klr Mthletics Instnt Workooks Series M Copyright 3P Lerning ii

3 Topic 1 - Modelling deprecition QUESTION 1 The grph elow shows how $1000 deprecites t the different rtes of 25% p.., 15% p.. nd 5% p.. over 8 yers. $1000 $900 $800 $700 5% $600 $500 $400 15% $300 $200 25% $ Time (Yers) Using the grph find: i the vlue of $1000 fter 6 yers t 5% p.. deprecition ii the mount y which $1000 deprecites in 3 yers t 25% p.. iii the deprecition of $1000 in the fifth yer t 15% p.. iv the slvge vlue of cr ought for $24 000, 4 yers go, t 15% p.. deprecition. Use the formul S = 1000(0.8) n to complete the tle of vlues, correct to two deciml plces. n S c The ove formul gives the vlue of $1000 if depreciting t 20% p... Sketch this on the ove grph. Mthletics Instnt Workooks Series M Copyright 3P Lerning 1

4 Topic 2 - Stright-line deprecition (1) QUESTION 1 Use the stright-line formul to find the current vlue of n sset where: purchse price $18 000, deprecition $750 per yer, fter 12 yers purchse price $9500, deprecition $1200 per yer, fter 5 yers. QUESTION 2 A usiness purchsed new delivery vn for $ Deprecition is llowed t $2500 per yer. Wht is the deprecited vlue t the end of 6 yers? Why wouldn t you use the ove deprecition llownce for 9 yers? Briefly explin. QUESTION 3 A 9 yer old mchine is currently vlued t $7500. If its purchse price ws $ find the mount of deprecition llowed ech yer. QUESTION 4 The curtins of house cost $ It is expected tht the curtins will hve n effective life of 10 yers nd will then e sold for $1500. Find: the nnul deprecition the nnul deprecition s percentge of the cost price. Mthletics Instnt Workooks Series M Copyright 3P Lerning 2

5 Topic 2 - Stright-line deprecition (2) QUESTION 1 Using the stright-line method of deprecition, $108 hs een pportioned ech yer on rotry hoe. The slvge vlue is $359 fter 5 yers. Find the purchse price of the rotry hoe. QUESTION 2 A frmer purchsed mchinery nd ssessed tht one mchine worth $ hd useful life of 8 yers. Its scrp vlue fter 8 yers ws estimted t $5000. The stright-line method of deprecition will e used. Clculte the nnul deprecition of the mchine. Complete the tle to show the slvge vlue fter ech yer. Yer Previous vlue Deprecition Slvge vlue 1 $ $5000 c Drw grph showing the slvge vlue over the eight yers. $ Slvge vlue $ $ $ $ Numer of yers Mthletics Instnt Workooks Series M Copyright 3P Lerning 3

6 Topic 3 - Declining lnce method (1) QUESTION 1 Use the declining lnce formul to find the slvge vlue of n sset with: purchse price $6000, deprecition rte 5% p.., fter 4 yers purchse price $24 000, rte of deprecition 8% p.., fter 7 yers. QUESTION 2 A cr ought for $ is depreciting t rte of 12% p.. of its vlue from the previous yer. Write down its slvge vlue (current vlue) fter 5 yers. QUESTION 3 Arnie ought trctor in 1998 for $54 000, which hs een depreciting t 15% p... Two yers lter he ought second trctor for $48 000, which hs een depreciting t 17.5% p... Which trctor hs the greter slvge vlue in 2008? Justify your nswer. QUESTION 4 The slvge vlue of mchine fter 10 yers is $5670. If it deprecited t the rte of 18.5% p.., wht ws the cost price (to the nerest dollr)? Mthletics Instnt Workooks Series M Copyright 3P Lerning 4

7 Topic 3 - Declining lnce method (2) QUESTION 1 A mchine ws purchsed for $ nd hd scrp vlue of $8500 fter 5 yers. Find its declining-lnce deprecition rte s percentge correct to 1 deciml plce. QUESTION 2 A mchine ought for $ deprecites t 20% p... Wht is its slvge vlue fter 8 yers, to the nerest dollr? Complete the tle to show the slvge vlue ech yer. (Give the slvge vlue to the nerest dollr.) Yer Previous vlue Deprecition Slvge vlue 1 $ c Drw grph showing the slvge vlue over time. $ $ Slvge vlue $ $ $ Numer of yers Mthletics Instnt Workooks Series M Copyright 3P Lerning 5

8 Topic 4 - Comprison of methods QUESTION 1 An industril sewing mchine ws ought for $ Using the stright-line method of deprecition, wht would e the vlue of the sewing mchine fter 5 yers if it is depreciting t $1500 per yer? Using the declining lnce method of deprecition t 20% p.., would the mchine e worth more or less fter 5 yers? Justify your nswer. QUESTION 2 A mchine, ought for $18 500, ws deprecited t 12% p... Wht ws the slvge vlue of the mchine fter 7 yers? Wht mount of deprecition per yer, using the stright-line method, would produce the sme result? QUESTION 3 A pump ws ought for $4600. Wht is it worth fter 1 yer if it deprecites y $483. Wht is this mount of deprecition s percentge of the cost price? c If the pump continues to deprecite t $483 per yer, how mny yers will it e efore the vlue of the pump flls elow $1000? d If the pump deprecites t the rte found in prt, how mny yers will it e efore the vlue of the pump flls elow $1000? (Use estimtion nd refinement.) Mthletics Instnt Workooks Series M Copyright 3P Lerning 6

9 Topic 5 - Deprecition s tx deduction QUESTION 1 John is contrctor who mkes round le silge. The tle elow shows the items he hs een depreciting, using the declining-lnce method, in his tx returns. The previous vlue is the vlue t the end of the previous finncil yer. Item Rte Previous vlue Deprecition Current vlue Trctor 1 10% $ Trctor 2 10% $ Hy rke 8% $5000 Bler 15% $ Mower 12% $8700 Wrpper 18% $ Complete the tle. Wht is the totl deprecition llowed s tx deduction? c If John ought second hy rke on Octoer 1, for wht frction of the finncil yer cn he clim tx deduction? d If the new hy rke cost $ nd is deprecited t 8% p.., find the mount he cn clim s tx deduction. QUESTION 2 Shron uses the stright-line method of deprecition. For computer tht she ought on Ferury 1, 2003 for $1800 she clims $150 s tx deduction. Wht is the slvge vlue of the computer on July 1, 2003? How much is the deprecition ech yer? c Wht is the vlue of the computer on July 1, 2006? QUESTION 3 Cmeron s Mowing Service ought new ride-on mower for $3600 on Septemer 1. Find the mount of deprecition the usiness cn clim s tx deduction on the next tx return if the declining lnce method is used t 12% p EXCEL HSC GENERAL MATHEMATICS REVISION & EXAM WORKBOOK Mthletics Instnt Workooks Series M Copyright 3P Lerning 7

10 Topic Test PART A Instructions 8 multiple-choice questions Ech question is worth 1 mrk Fill in only ONE CIRCLE Clcultors my e used Time llowed: 10 minutes Totl mrks = 8 1 An sset deprecites using the stright-line method. If its purchse price ws $9750 nd its slvge vlue is $2175 fter 6 yers, how much is the mount of deprecition pportioned per yer? A $1625 B $ C $ D $ Furniture vlued t $ deprecites t rte of 10% p.., find the vlue of the furniture fter 3 yers. A $ B $ C $ D None of these 3 The vlue of cr deprecites y 12% of its vlue ech yer. If its price ws $ when new, wht will e its vlue (to the nerest dollr) t the end of 5 yers? A $ B $ C $ D $ A truck ws ought for $ on April 1. If it deprecites using the declining-lnce method t 15% p.., the mount of deprecition tht cn e climed s tx deduction tht finncil yer is closest to: A $9980 B $3460 C $3260 D $ A qud ike deprecites y $750 per yer. If its slvge vlue fter 7 yers is $3000, its purchse price ws: A $8250 B $9000 C $7500 D $ Ech yer computer deprecites y 20% of its vlue t the eginning of tht yer. A new computer costs $4300. Wht will e its vlue t the end of the second yer? A $2752 B $2863 C $2850 D none of these 7 A vn ws ought 6 yers go nd hs een depreciting using the declining-lnce method t 12% p... Its slvge vlue is $ Its purchse price ws closest to: A $ B $ C $ D $ A chinsw is deprecited y the stright-line method, with $85 eing pportioned ech yer. The purchse price of the chinsw ws $690 nd its current slvge vlue is $180. How old is the chinsw? A 4 yers B 5 yers C 6 yers D 7 yers Totl mrks chieved for PART A 8 Mthletics Instnt Workooks Series M Copyright 3P Lerning 8

11 Topic Test PART B Instructions This section consists of 5 questions Show ll necessry working Time llowed: 15 minutes Totl mrks = 12 9 An overlocker is ought for $675. It is deprecited using the stright-line method. The mount of deprecition llocted in the first yer is 10% of the purchse price. 1 mrk ech Find the mount of deprecition pportioned ech yer. Find the slvge vlue of the overlocker fter 5 yers. 10 A usiness uys new mchinery for $ tht deprecites t the rte of 20% of its previous vlue ech yer. After three yers, find: 1 mrk ech its slvge vlue the totl mount of deprecition. 11 Furniture ws purchsed for $ nd hd slvge vlue of $4000 fter 7 yers. 2 mrks ech Find the mount of deprecition pportioned per yer if the stright-line method ws used. Mthletics Instnt Workooks Series M Copyright 3P Lerning 9

12 Find the rte, s percentge correct to 1 deciml plce, if the declining-lnce method ws used. 12 Find the mount of deprecition tht cn e climed on the tx return if pressure clener ws ought for $868 on Mrch 1 nd the stright-line method of deprecition is to e used, pportioning $180 ech yer. 2 mrks 13 A tle lmp, costing $1500 when new, deprecites t the rte of 20% of its previous vlue ech yer. After how mny yers will its vlue e pproximtely $300? (Mke n estimte nd refine.) 2 mrks Totl mrks chieved for PART B 12 Mthletics Instnt Workooks Series M Copyright 3P Lerning 10