Question

A bond has a coupon rate of 2.1% and pays coupons semi-annually. The bond matures in 4 years and the yield to maturity on similar bonds is 3.7%. What is the price of the bond?

Answer 1

Price of Bond = C * [( 1 - ( 1 + R)^-N) / R] + FV / ( 1 + R)^N

Where, C = Coupon Payment

R = Yield Per period

N = Number of periods till maturity

FV = Face value

Yield Per period ( Semi - Annually) = 3.7% / 2

= 1.85%

Coupon Payment = Face value * Coupon rate * ( 1 / Number of compounding)

= 1000 * 2.1% * ( 1 / 2)

= 10.5

Number of Periods = 4 * 2

= 8

Price of bond = 10.5 * [( 1 - ( 1 + 1.85%)^-8] / 1.85% + 1000 / ( 1 + 1.85%)^8

= 10.5 * [( 1 - (1.0185)^-8] / 0.0185 + [1000 / (1.0185)^8]

= 10.5 [( 1 - 0.86359820) / 0.0185] + [1000 / 1.157945892]

= 10.5 * 7.373070270 + 863.598210

= 941.02 [ rounded to two decimals]

Price of bond is 941.02