What must be the price of a $1 bond with a 6.8% coupon rate, semiannual coupons, and eight years to maturity if it has a yield to maturity of 8% apr?

Coupon (R) = 6.8% x 10,000 = $680

Face value (FV) = $10,000

Number of times coupon is paid in a year (m) = 2

No of years to maturity = 8 years

Yield to maturity (Kd) = 8% = 0.08

Po = R/2(1- (1 + r/m)-nm) +  FV/ (1+r/m)n m

                      r/m

Po = 680/2(1-(1+0.08/2)-8x2) + 10,000/(1 + 0.08/2 )8x2

                          0.08/2                              

Po = 340(1 - (1 + 0.04)-16)    + 10,000/(1 + 0.04)16

                      0.04                            

Po = 340(1-0.5339) + 10,000/1.8730

                 0.04

Po = 3,961.85 + 5,339.03

Po = $9,300.88

Explanation:

The current market price of a bond is a function of the present value of semi-annual coupon and present value of the face value. The present value of semi-annual coupon is obtained by multiplying the coupon by the present value of annuity factor at 8% for 8 years. The present value of face value is obtained by discounting the face value at the discount factor for 8 years. The addition of the two gives the present value of the bond. All these explanations have been captured by the formula.

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