The price of a bond with an 8% coupon rate paid semi-annually and a par value of

Question

The price of a bond with an 8% coupon rate paid semi-annually and a par value of $1,000, and fifteen years to maturity is the present value of
A) 15 payments of $40 at 6 month intervals plus $1,000 received at the end of the fifteenth year.
B) 15 payments of $80 at 6 month intervals plus $1,000 received at the end of the fifteenth year.
C) 30 payments of $40 at 6 month intervals plus $1,000 received at the end of the fifteenth year.
D) 30 payments of $80 at 1 year intervals plus $1,000 received at the end of the 30th year.
Answer: C
answer is c, but why is the payment 30 and not 40, that is what i dont understand

Explanation / Answer

Semiannual Coupon payment = 8%*1000/2=$40 No of years to maturity = 15 years No of semiannual payments = 15*2 =30 payments Price = 40/(1+r) + 40/(1+r)^2 +........ 1004/(1+r)^30 Answer C) 30 payments of $40 at 6 month intervals plus $1,000 received at the end of the fifteenth year.

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