Question

A bond has a face (par) value of $10500; it will mature in 5 years. The bond coupon rate is 1.50%; there are 5 premium payments per year. If the bond is purchased for 95.08% of its face value and later sold at its face value, what is the bond yield rate per period?

Answer(0.51)

Please show all work

Answer 1

We can compute periodic YTM for a bond using following formula.

Periodic YTM = [C + {(F - P)/N}] / [(F + P)/2], where

C: Periodic coupon payment = $10,500 x 1.5% x (1/5) = $31.5

F: face value = $10,500

P: Trading price = $10,500 x 95.08% = $9,983.4

N: Compounding periods till maturity = 5 x 5 = 25

Therefore,

YTM = [31.5 + {(10,500 - 9,983.4) / 25}] / [(10,500 + 9,983.4) / 2]

= [31.5 + (516.6 / 25)] / (20,483.4 / 2)

= (31.5 + 20.664) / 10,241.7

= 52.164 / 10,241.7

= 0.0051

= 0.51%