Estimate the percentage price change for a 5-year $1,000 par value bond,with a 6% coupon,if the yield rises from 8% to 8.5%.Interest is paid semiannually.
A) 2.1%
B) -2.1%
C) 4.4%
D) -4.4%
E) None of the above

Question

Quizplus · Accepted Answer

The price of the bond = $918.89 =
 $30 \left( \frac { 1 - \frac { 1 } { 1.04 ^ { 10 } } } { .04 } \right) + \frac { 1000 } { 1.04 ^ { 10 } }$ 
The present value of the weighted cash flows = $8015.41 =
30/(1.04)+ 60/(1.04)² + 90/(1.04)³ + 120/(1.04)⁴+150/(1.04)⁵
+ 180/(1.04)⁶ + 210/(1.04)⁷ + 240/(1.04)⁸ + 270/(1.04)⁹ + 10300/(1.04)¹⁰
Macaulay duration = 8015.41/918.89 = 8.72
Or 8.72/2 = 4.36 years
Modified duration = 4.36/(1 + .04)= 4.19 years.
%price change = -(4.19 × 0.5)= -2.1%

Estimate the Percentage Price Change for a 5-Year $1,000 Par