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(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
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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 .
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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
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5f Quay”)? ﬁgfég’: (’4’ 2993;” (Wu/‘68 DMRQJLWS LO”) \\ wngISSD 2‘; /Q/4)€?<’3</I+ ﬁgf} .2, /b /Z/0./9 2
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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
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‘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.
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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 UniversityWest Lafayette.
 Fall '08
 Staff
 Math

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