Question

^{Calculate the duration for the following bond, remember: D =- INt* CFt Lt=1 (1 + r)t_t=1t * PV+ _Et=1t * PV¢ EX=1 PVE t=1 (1 + r)t IN CE V Calculate the duration by filling out the table below. Then calculate the duration. t CFt DFt CFt * DFt CFt *t* DFt 8.0% 9.0% 101 102 103 104 105 106 107 Coupon Rate Rate of Return Semiannual Par Value Price Check Duration No $ 1,000 $961.10}

Answer 1

2 1 32 43 5 4 DFt =1/1.09^A2 =1/1.09^A3 =1/1.09^A4 =1/1.09^A5 =1/1.09^A6 80 80 1080 CFt*DFt =C2*B2 =C3*B3 =C4*B4 =C5*B5 =C6*B6 =SUM(D2:06) CFT*t*DFt =D2*A2/$D$7 =D3*A3/$D$7 =D4*A4/$D$7 =D5*A5/$D$7 =D6*A6/$D$7 =SUM(E2:E6) 7 8

A 1t CFt 2 1 $ - 2 $ 3 $ 4 $ 5 $ B C D DFt CFt*DFt CFT***DFt 80.00 0.9174 $ 73.39 0.076364821 80.00 0.8417 $ 67.33 0.140118937 80.00 0.7722 $ 61.77 0.192824225 80.00 0.7084 $ 56.67 0.235870612 1,080.00 0.6499 $ 701.93 3.651666581 $ 961.10 4.296845176

DFt = discount factor = 1/1.09^t

Price is sum of all CFt*DFt = $961.10

Column E is CFt*DFt*t/price of coupon.

Duration of bond is sum of duration of all coupon.

So, Duration of bond = 4.30 years.