1.A. Yahoo bond pays coupon interest 2.75% semi-annually on face value $100. Bon
ID: 2789997 • Letter: 1
Question
1.A. Yahoo bond pays coupon interest 2.75% semi-annually on face value $100. Bond is sold on November 14, 2017. Bond matures in April 14, 2035. Bond is priced to yield the investor 2.80%.
How much is the bond’s price (clean)?
How much is the bond’s accrued interest?
How much is the bond’s dirty price?
B. A US Treasury note with interest rate 3.10%/ matures on Aug 15, 2020 pays semi-annually on face value $100. Bond is purchased on December 3, 2018. Bond is priced to yield the investor 3.20%.
How much is the bond’s price (clean)?
How much is the bond’s accrued interest?
How much is the bond’s dirty price?
******* Intrerest payment date is not mentioned, the question should be solved without knowing that.
Explanation / Answer
Problem 1A:
Previous coupon date: Apr 14, 2017
Immediate previous coupon date: Oct 14, 2017
Settlement date: Nov 14, 2017
Maturity date: Apr 14, 2035
Coupons are paid semi-annually.
Time between coupon payments: T = 0.5 year or 1 semester
Time between Oct 14, 2017 and Nov 14, 2017: t = 1/6 semesters
t/T = 1/6
N = 2*(35 - 17) - 1 = 35 semesters
FV = $100
PMT = 100*0.0275/2 = $1.375
r = 2.80/2 = 1.40%
PV = (1.375/0.014)*(1 - 1/1.014^35) + 100/1.014^35 = 99.311985
PV (Full) = PV*(1 + r)^(t/T) = 99.311985*1.014^(1/6) = 99.542373
Dirty price = $99.54
Accrued Interest: AI = PMT*(t/T) = 1.375/6 = 0.229167 = $0.23
PV (Flat) = 99.542373 - 0.229167 = 99.313206
Clean price = $99.31
Problem 1B:
Clean price = $99.83
AI = $0.93
Dirty price = $100.76
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