Question

How much would you pay for a bond that has a 4% coupon rate, matures in 15 years and market interest rates have risen to 6%? (use semiannual payments)

Please Explain

Answer 1

Price of a bond is present value of all cashflows associated with the bond - namely coupons and maturity value, discounted at market rate of interest.

Mathematically, it is represented by formula:

where P is the price of bond, C is the periodic coupon, i is the periodic YTM, M is the face value, n is number of periods to maturity.

Assume, for the bond in question, Face value M to be $100,

C = 4% * $100 = $4 (annually) --> $2 semi-annually

n = 15 years --> 30 semi-annual periods

YTM = 6% (annual) --> 3% semi-annual

Substituting values in formula,, we get

P = $80.40

So, for a face value of $100, we should be paying $80.40.

For a face value of $1000, we should be paying $804.