Question

a $1,000 face value bond currently has a yield to maturity of 6.03 percent. The bond matures in thirteen years and pays interest semiannually. The coupon rate is 6.25 percent. What is the current price of this bond

Answer 1

Answer:

The current price of the bond is $1019.63

Explanation:

The current price of the bond is the present value of the face value of the bond that will be received at maturity plus the present value of the interest payments that the bond will provide.

The interest payments by the bond are of equal amount and after equal interval of time and are for a defined time period. Thus, they can be treated as an annuity and the present value of annuity can be calculated using the interest payments.

The semiannual interest payment by bond is = 1000 * 0.0625 * 6/12 = $31.25

The semi annual YTM = 6.03 / 2 = 0.03015 or 3.015%

The total discounting periods are = 13 * 2 = 26 periods

The current price of the bond = 31.25 * [ (1- (1+0.03015)^-26) / 0.03015 ]  +

1000 / (1+0.03015)^26  

Current price of the bond = $1019.63

Answer 2

Answer:

$1,020

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond.

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 6.25% = $62.5 annually = $31.25 semiannually

Number of periods = n = 13 years x 2 = 26 period

YTM = 6.03% / 2 = 3.015%

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ $1,000 / ( 1 + r )^n ]

Price of the Bond = $31.25 x [ ( 1 - ( 1 + 3.015% )^-26 ) / 3.015% ] + [ $1,000 / ( 1 + 3.015% )^26 ]

Price of the Bond = $557.69 + $461.94 = $1,019.63 = $1,020