Question

A bond has a $1,000 par value and an 8 percent coupon rate. The bond has four years remaining to maturity and a 10 percent yield to maturity. If the bond yield would decrease by 0.3 percentage points, the estimated percentage change in price of the bond would be ________%.

Answer 1

Current price of the bond at 10 % discount rate = $ 1,000 x 8 % x [ { 1 - ( 1 / 1.10 ) ⁴ } / 0.10 ] + $ 1,000 x ( 1 / 1.10 ) ⁴ = $ 253.59 + $ 683.01 = $ 936.60

If the discount rate is 9.7 % , price of the bond = $ 80 x [ { 1 - ( 1 / 1.097 ) ⁴ } / 0.097 ] + $ 1,000 x ( 1 / 1.097 ) ⁴ = $ 255.24 + $ 690.52 = $ 945.76

Estimated percentage change in price of the bond = $ ( 945.76 - 936.60) / $ 936.60 * 100 = 0.98 % increase.