Question

114. You purchase a bond with a coupon rate of 8.13 percent, semiannual coupons, and a clean price of $998.40. If the next coupon payment is due in two months, what is the invoice price? A. $1,018.90 (lean price = invoice price-1鏢期陇应計 B. $1,019.36 C. $1,001.60 998.4O in voice price -20,5 D. $1,027.67 E. $1,004.33 4 r: 6,15% invoice Price : 1018,90 #

how to solve

Answer 1

Invoice Price = Clean Price + Accrued Interest

= Clean Price + (Coupon Rate/2)*(Days Passed/Total Days)*(Face Value)

= 998.40 + (0.0615/2)*(2/3)*Face Value

= 998.40 + (0.0615/2)*(2/3)*1000

=998.40 + 20.5

=1018.90

So the correct answer is A. 1018.90$

Notes : 1. Since the Coupons are Semi Annual, the rate is divided by 2

2. Derive 2/3 : Since the next coupon is due in 2 months i.e. 4 months are already passed out of 6 months. (4/6)

Assumptions : 1. Since the Face value of the bond is not given which should be given in the ideal conditions, it is assumed to be 1000$

2. Since Interest Rate is not given in the question, another way to solve the question could be to assume coupon rate as equal to the Interest rate . If we assume coupon rate as equal to interest rate, it means Clean Price equals Face Value. By solving this, the answer to the question would still come to 1018.8672 which again gives you the A option as answer.