Question #50865

A 30-year maturity bond with face value of $1,000 makes annual coupon payments and has a coupon rate of 8%. What is the bond's yield to maturity if the bond is selling for $1,100?

Expert's answer

A 30-year maturity bond with face value of B = $1,000, r = 8%, P = $1,100.

c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P, where

c = annual coupon payment (in dollars, not a percent)

Y = number of years to maturity

B = par value

P = purchase price

In our case:

80/(1 + r) + 80/ (1 + r)^2 + … + 80/ (1 + r)^30 + 1,000* (1 + r)^30 = 1,100

So, YTM = r = 7.18%

c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P, where

c = annual coupon payment (in dollars, not a percent)

Y = number of years to maturity

B = par value

P = purchase price

In our case:

80/(1 + r) + 80/ (1 + r)^2 + … + 80/ (1 + r)^30 + 1,000* (1 + r)^30 = 1,100

So, YTM = r = 7.18%

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