First, compute the current price of the bond as:
FV = $1,000; PMT = $70; N = 18; I/Y = 8%; CPT → PV = –$906.28
Next, change the yield by plus-or-minus the same amount. The amount of the change can be any value you like. Here we will use ±50 basis points.
Compute the price of the bond if rates rise by 50 basis points to 8.5% as:
FV = $1,000; PMT = $70; N = 18; I/Y = 8.5%; CPT → PV = –$864.17
Then compute the price of the bond if rates fall by 50 basis points to 7.5% as:
FV = $1,000; PMT = $70; N = 18; I/Y = 7.5%; CPT → PV = –$951.47
The formula for effective duration is:
(V- – V+) / (2V0Δy)
Therefore, effective duration is:
($951.47 – $864.17) / (2 × $906.28 × 0.005) = 9.63.
