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Quiz4Sol - ACTSC 231 i Fall 2009 1[5 marks(a[2 Arrange...

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Unformatted text preview: ACTSC 231 i . Fall 2009 1. [5 marks] (a) [2] Arrange these annuities into order from smallest to largest and explain briefly: d(fi|4)> am, a'(—\2)a 5m: a'gnle): 0%) (1 [Li < (m ._ ~— on “(‘0 SthGL [Culver [>qu{—; w‘vH/w'k each gear mgr/Ug— wx- . kloW PJ- (b) [3] An annuity paying $50 at the beginning of every year for n years costs $1000. An annuity paying $1 at the beginning of every year for k years costs $Y (Assume k is a factor of n.) i. : Derive an expression for the present value of an annuity paying $1 at the beginning of every k: years for n years. W- ._ 01‘ . a El = Y . ’ a; ' ET ° k 7“; “ El W Q Nae, A, '[ ' , (- I é: in 1H l? l " - fl \Y W “C we MM ijwwrls‘ 0‘? X Oil m bej‘V‘V‘h"? “X M «K mourn-11M, ~1er 15 Xm’i :z/O k 21:71.40, 'Fbt/ 'l‘l/VCS 'er {06.16‘viUOLW/C'l‘ / X: dB :\_(¢>“/’“_<1-v“i/_e so at M :15 z, Z11 w ii. Evaluate this expression if Y = $5.57. Hint: You do NOT need n, k, or the 7&3 Y interest rate. l .—‘ Ki) ACTSC' 231 I Fall 2009 2. [9 marks] A 10% $1000 semiannual coupon bond redeemable in 10 years is bought to yield in) = 8%. The premium on the bond is $108.72. Assume each month is 1/12 of a year. - (a) [3] Find the redemption amount and the price of the bond. '7 2 <1 7' 10%.?2. (WWW) ( 'bcxs‘t Q, €>m~v\m> {)L’[ [05120 : fiat 516+ Macaw: _ * __, é7asw~tor72 : v ' eLLur [”3 [_ orifiéfi} :El050\ [email protected][ (b) [2] Find the amount of interest in the 7th coupon payment. . . H E6: SQ<XFflfi%”"lOSOV : i [ [3 L[ ' 5 C) .. so 7 : 5’39 we 7 \l%f[6€> ==~ [73075: $753 ”'7 (c ) [2 2Find] the dirty priceZ years and )Omonths after purchase " o - 7— 26 9" 3’ leZm—l 7W FMfi‘O- @402, . - - ‘/~ D51; = <56 + BOW/3 (d) [2] Using whatever method you choose, find the clean price on this date. Specify which method you used meme 1 [strata Cot/Vin) Va) figs (EL 550 V OMAUJ WM 2.. ($lrmbk% MM ? “(SHCOJ C [Jul-n.) OM BS : SO Ok'afiwya + [0 SO \I‘S’g’wfi Of; ‘. 3;“; ”L €35 “* EEC : WMA. 3 (Gm u’L’\1v\,J/bv J / ‘l’WvQéfiCmfi-wfi CCV'\) vv\~ (’C‘Sk’ C :— 50 ‘1‘" 35% ; C CL"'[+1050\/H3 ACTSC 231 Fall 2009 ‘3. [6 marks] A 6% $1000 semiannual coupon bond is callable at the end of 4, 4.5, or 5 years for $1025, $0, or $1000, respectively. You want to guarantee yourself an annual yield of at least 5% convertible semiannually. (a) [4] If the price you are willing to pay for this bond is $1043.76, find the rangevof possible valuefifor C (the redemption amount if the bond is called in 4.5 years.) Ya" 30 093”in + KOZSV7’ : l0 347331, PS 1 $0 OVEZJ‘Z + lODO-Vlo : 10ng\:fé 8013,,- 3 lessee 1., area «a.» ' lolly“ J“ 53' 11* ”Mos 13w Mia Foss. ALS'IACL 30v WKAA' POMS m Miklmm> - 51 - - “D- ..f CC 2 mafia-7t _ 2.3a.1aé 1C Zhlflfl.%l .\ . f No‘ln‘il (Ude- A20 1420" OkQ‘lVO.“ Mach flats 4; link lawl— ii sou ‘chludzcl Mel (Kas‘h/i flow '50, 'l’l/xorl ‘5 ‘0 K. > . (b) [2] NOW suppose there are no call premiums (i.e. the bond is always redeemable for $1000.) Without doing any calculations, explain in one or two sentences which would be the worst possible call datefor the bond. ’WS “‘5 0» ‘TwZ,wvl_~/\~y bowA s'\«\C,2,.. +lNL lAW’S-l— (OER is \cwéxr “HAM/c «HA-6. cmfow. rock- The, wafS‘l’ vessel MAL Call Agni—e. wad d Se, Ll gears: 51 no; excl/k (bu-YO“ COL/Clout A3 CK bra Faill/Ml 3 WA \IJL' WWW—3V W AF) Cfiwmmw 11,3 (ox/j as «two $31 loLJL , ...
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