MA373 F11 Chapter 9 Homework Solutions

MA373 F11 Chapter 9 Homework Solutions - @9439 W; if” Q...

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Unformatted text preview: @9439 W; if” Q (:3 I QM KB QKNXE 00@ E mo / {00 N c: ; PW; 1m: / -—L i Fvg/Qw V @153 : #95771. 24 0000 a}: £722“ “Ema: % @mmm MOO «Mt Pwuagg 91/000 V ‘ M. x.“ 36mg VI 96%, Mam: g; /WJ / jjgmmh “1% Pfafii‘cggtéw (/¢,3@>g3¢a5%%¥ “pmég % I tug/@391. av .30 (77%;? wk» icy/9,4? 7H4 s»w;.7awzwgo2v> 74” WWWOW” fl Mj’aé. 4/5 D/f7ZQ/6fl46; 4% , mud/Y5 7 (3 33818.62; 5559:? 95 self. = 5235351 5. Wang Life Insurance Company issues a three year annuity that pays 40,000 at the end of each year. Wang uses the following three bonds to absolutely match the cash flows under this annuity: a. A zero coupon bond which matures in one year for 1000. b. A two year bond which matures for 1200 and pays an annual coupon of 100. This bond ls priced using an annual yield of 7%. ' c. A three year bond which matures for 2000 and pays annual coupons of 75. This bond‘ has a price of 1,750. it cost Wang 104,000 to purchase all three bonds to absolutely match this annuity. Calculate the one yearspotinterest rate. ‘ ’8) av W 'thAa/‘m “A: 49ml W PrIQP a die 0% i" l 0‘0”? W 2st? (Bo‘wl 6Q to M'me WM 5,0 Mai.” WJDOD (All, N: 2_ meleD Fucizoo TN: 7 arr PV=in832$3 *Pe-t'c E.» “75’ i750 l 9 . 177l08<l3>fl75¥qw IQ”) is (I 300) t( Imsy‘é to bloom? ‘Ll‘l‘ww M at 2; M \f C? '30 a) \ p 4 .fl. beamwgg..msga ' '~ 2 [WA Qr—‘LQ'IPS 7” s a rite/000 b M) +Q(107~»§ a (0) + Q (moo) 4— (1‘1 @9039?)th + l‘f.277l0843(7»’5=%0,° m 105' 70%? 93009) — i9. l77)b$¥5(z{) .. . z I 000 a m 55 . {88597 89 F Fame: at: a: 33/ 739.99 K ; “W WW “Wain: E/ W , , ; x a , , ~ 00 5 50C) 5400 W Q 2%“; ‘ 9,24% 25’” U ~ a?» :90 (’1’ “P / v \ij [/QQQ v m 7 gL/SZQZW l (3? N effiifi! 9m? “L m Q : 5 9:; <49 V “956%?!” a M t... W \”Tr+»?vmvfm~ , "PW . five year bond matures for 20,000. The bond pays coupons of: i. 3000 at the end of the first year, ii. 1500 at the end of the second year, 0 m. 1000 at the end of the third year, 0 0 ea” iv. 750 at the end ofthe fourth year, and 00 ‘490 \oo 4.0/0 [900 v. 600 at the end of the fifth year. ) I: ‘ . % Calculate the Macaulay Duration of this bond at 5%. 0 l ‘3' "3 L9 5‘ Z Q42 HDM'E “130,023: W . 2.,(3.l.,\l§ awe/l) V 9%]st l e: l ~',I ’ q r , f ‘ (r V§ ‘ 2m— aooozzb E 00:3 __ f W " b 5000 (y+\)‘v+\;5+v‘l+v$ + l00,000\/ w . gooov + )soovz' + )000V}+750\qu,10600\l l r . - (0(0 : ; Bldg)!” )4 83‘] . IQOS’E “Pmflg aw “5:353 3-? Cur/gm} (QM/g (I W [Maj/(2%] Dqu7LM>aWA® $3” Cugfié’k)? (/‘fi' V/mAMMQ‘Q Edgy/.Ob‘i‘sflf—no7j 5f Quay”)? figfég’: (’4’ 29-93;” (Wu/‘68 DMRQJLWS LO”) \\ wngISSD 2‘; /Q/4)€?<’3</I+ figf} .2, /b /Z/0./9 2 ‘ “f2. l w W ’ W ) V 512700946 m w f g gmb 3 ” WWW?! % $ aw/ 373,85 3 m /€“QW , 43:1: ‘4 W "““ 0,63 Bard}; 9) «3/ (ML [09?(QDW 5/5“? 9 mfiaadém Gomveyzj‘éy 3: W W lmfia\i M) W? 2w (ON) f W )0Q (52?? W )v4~QV‘k9v3+/¢vg+g5vf @Wéfi 3 /00 \f + /00/w2)[3)v2+ IDOBy'DV 7” {’00 {wk/Q V 1”” /0Q€/5;}i/éfl> V5 gufiwg % An annuity has the following payments: a. A payment of 1000 at the end of year 1 b. A payment of 5000 at the end of year 3 c. A payment of 2000 at the end of year 6 Calculate the modified convexity for this annuity at 6%. i I i E :3 /5./Liz+¢i W ti} wgfiflfiggj ” 3’ /0 7 3, éa @ Egvlfgm . “ ' z. flag/QT mhwrev" «223 e ’90?” ‘F )mé " \L L9+<®Z§igr®(@wg> acque owns the following portfolio. Macaulay Duration 50,000 m 30,000 20,000 The prlce, Macaulay Duration, and Macaulay Convexlty were calculated at an annual effectIVe rate of 5%. Calculate the Modified Convexity of this portfollo. m/lo cowl) + W“ “2' ) 5 Mod) @5110 M0”); " (\l‘ 2; Q “W 2 cf nit CORN ’ "52"???" I: )DOI DOC) Fm (Pomumwo =9 28(4)“ 0 (Qt-93°00) m 4 L, J“ (3560; 000) *Lll'fl’o’ 003+ MK ‘2’ 15%.? V mama FOE » fir / ~ LID t } foflfl‘o ‘ I, 93 9.101%?) ’ ' MOD CONU v My 50 29% I} ‘10:); ’7 /Oq00 /?V 05 Q 47 (Logs: S (93) 0”“?4’ f +m :: Q5,D’[0~C}é9 .1: "Frags §g% €5ao£ Ip/sawfimfi Mr» (air) @ rs: 4:2; % LHI’ +353: (as, mm; :3 Wmfifi‘gfim «WWI u :3) I; 43;: )5‘0, 412153"?! .k M “00 O .\ July » igLQ—o—I: 294,599.90 (/ .0 5’); c) a+‘/b:Bq-+—3b »’ bslq ’— 3c2= 2M,e999/ :30“: gglggq,éz/ I77,7¢’9’-2‘7 /'\ MM ,4 W; BoD’D bnga: ...
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This note was uploaded on 02/26/2012 for the course MA 373 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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MA373 F11 Chapter 9 Homework Solutions - @9439 W; if” Q...

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