A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.6%, and sells for $1,140. Interest is paid annually. (Assume a face value of $1,000 and annual coupon payments.) a. If the bond has a yield to maturity of 9.4% 1 year from now, what will its price be at that time?

Price of bond=948.8583731

Explanation:

The value of the bond is the present value(PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).

Value of Bond = PV of interest + PV of RV

Semi-annual interest = 8.6% × 1,000 × 1/2 =43

Semi-annual yield = 9.4%/2=4.7 %

PV of interest payment

PV = A  (1- (1+r)^(-n))/r

A- 43, r-0.047, n- 20

= 43× (1-(1.047)^(-10)/0.047)

= 549.7724893

PV of redemption Value

PV = F × (1+r)^(-n)

F-1000, r-0.047, n- 20

PV = 1,000 ×   1.047^(-20)

PV = 399.0858837

Price of Bond

549.772 + 399.085

=948.8583731