Question

suppose a five year $1000 bond with annual coupons has a price of 899.44$ and a yield to maturity of 5.6% , what is the bond's coupon rate?

Answer 1

Sol: Face value of the Bond (FV) = $1000

Maturity of the bond (N) = 5 years

Current Price of the bond(PV)= $899.44

Yield to Maturity(YTM) = 5.6%

We are required to compute the Coupon rate (r) of the annual coupon bond,

Formula for Coupon rate (i.e., the Interest rate on a bond)

= Sum of coupon payments(PMT) / Face Value(FV)

Sum of coupon payments(PMT) =   Current Price of the bond(PV= $899.44) *   Yield to Maturity(YTM) = 5.6%

= $899.44 * 5.6%

= $50.37 (apporx) or let PMT = $50

Coupon rate of bond = PMT / FV

= $50.37 / $1000 or $50/ $1000

Therefore bond's coupon rate   = 5.036% or 5%

Summary: If we purchase a five year maturity bond of Face value $1000 at current market price of $899.44 having a an annual coupon rate of 5.036%(approx), then we can get Yield to maturity of 5.6%.

Thank you.