Question

A $100 par value 10-year bond provides coupons at 5% convertible semiannually. The yield rate is 4% convertible semiannually. What is the flat price 8.4 years after issue at the same yield rate (assuming compound interest)?

Answer 1

Flat price meaning is clean price, without accrued interest between two coupon payment.

Dirty price= Flat price + Accrued Interest

Flat price after 8.4 year means, Dirty price after 8.4 years = Flat price (after 8 years) + Accrued interest of coupon (coupon payment of 0.4 year period after 8 years)

Here the Flat price is bond price after 8 years when bond maturity will be 2 years.

T= 2 years, c = 5% annually , Yield = 4 % annually , i = 4/2 = 2% semiannually

n= period = 4 (semiannual payment)

Coupon payment semiannually, C = $2.5, M = Face Value = 100

Bond Pricing formula,

solving this formula,

P = 9.52 + 92.38

P = $ 101.90

Flat price = $101.90