Question

A $1,000 par value 8% bond with quarterly coupons is callable five years after issue. The bond matures for 1000 at the end of ten years and is sold to yield a nominal rate of 6 percent compounded quarterly, calculated under the assumption that the bond will not be called, and is redeemed at maturity. Please determine the call premium at the end of five years, that would yield the purchaser the same nominal rate of 6% compounded quarterly if the bond is, in fact, called at the end of five years. （please no excel formulas and financial calculator)

Answer 1

8% of 1000= 80 is the coupon compounded quartely= 20 per quarter

6% is the nominal rate of interest coumponded quartely= 1.5% per quarter

1000 is the Face Value

number of years= 5*4=20(since coumpounded quartely)

let K be the present value of this bond

K= 20/(1.015) + 20/(1.015)^2 + 20/(1.015)^3.........+ 1020/(1.015)^20

k=1085.84

hence, call premium= 1085.84-1000=85.84