Question

A $1,000 6% n-year par-value bond has annual coupons. Tabitha bought the bond to yield 5%. The amount of interest in the first coupon is $52.89. Calculate the amount of premium Tabitha paid for the bond.

Answer 1

Given,

FV = $1000

coupon = 6% of 1000 = $60

YTM = 5%

time to maturity = n

interest in 1st coupon = $52.89

So, using I1 = C - (C-Cj)*(1+YTM)^-n

So, 52.89 = 60 - (60-50)*(1.05^-n)

1.05^n = 1/0.711 => n = 7 years.

So, year to maturity of the bond = 7 years.

So current price is sum of PV of coupons and PV of face value

So, Price = 60/1.05 + 60/1.05^2 + 60/1.05^3 + 60/1.05^4 + 60/1.05^5 + 60/1.05^6 + 1060/1.05^7 = $1057.86

So premium on the bond = 1057.86-1000 = $57.86