Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 7.7%. What is the duration if the yield to maturity is 11.7%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)
YTM Duration 7.7% YTM 11.7% YTM
Calculation of Duration
PV Rate @ 7.7% 

Following data are available 

Face Value 
1000 
(Assume) 
Coupon Rate 
6% 

Years to maturity 
3 
years 
Redemption Value 
1000 

Yield to maturity 
7.70% 
First step : Calculate market price of bonds 

60, present value 7.7% for 3 years) 
60*2.59 
155.4 

1000, present value 7.7% for 3 years) 
1000*.800 
800 

Market Price 
955.4 

Second Step: Calculation of bond 

Year 
PV @7.7% 
Proportion of bond Value 
Proportion of bond value x time 

1 
0.928 
55.68 
0.05828 
0.05828 
2 
0.862 
51.72 
0.05413 
0.10827 
3 
0.8 
848 
0.88759 
2.66276 
955.4 
1 
2.82931 

Duration of bonds is 2.8293 years 
PV Rate @ 11.7% 

Face Value 
1000 
(Assume) 

Coupon Rate 
6% 

Years to maturity 
3 
years 

Redemption Value 
1000 

Yield to maturity 
11.70% 

First step : Calculate market price of bonds 

60, present value 11.7% for 3 years) 
60*2.4113 
144.678 

1000, present value 11.7% for 3 years) 
1000*.7162 
716.2 

Market Price 
860.878 

Second Step: Calculation of bond 

Year 
PV @11.7% 
Proportion of bond Value 
Proportion of bond value x time 

1 
0.8947 
53.682 
0.06236 
0.06236 

2 
0.8005 
48.03 
0.05579 
0.11158 

3 
0.7162 
759.172 
0.88185 
2.64556 

860.884 
1.00000 
2.81949 

Duration of bonds is 2.8195 years 

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