Question

A 10.2%, 18-year bond is quoted at 104.75. Calculate the current yield and yield to maturity on this bond.

Answer 1

Coupoun amout = 1000*10.20%
$102
Bond price = $1000*104.75%
=1047.5
Current Yield = Coupon amount / bond price
=102/1047.5
=9.74%
Bond price =C*[1-(1+YTM)^-n / YTM] + [P/(1+YTM)^n]
Where,
C= Coupon amount
YTM = Yield To maturity
n = Number of periods
P= Par value
$1047.5=102 * [1 - (1 + YTM)^-18 / YTM] + [1000 / (1 + YTM) ^18]
1047.5/102 =[1 - (1 + YTM)^-18 / YTM] + [1000 / (1 + YTM) ^18]
10.2696=[1 - (1 + YTM)^-18 / YTM] + [1000 / (1 + YTM) ^18]
YTM =	9.63%