Question

The present value of a stripped $100,000 24 month 1.79% Treasury Note is $95,343.91. What is the 24 month zero coupon yield (rounded % to three places after the decimal?

Answer is: 2.85 How do you get this answer?

Answer 1

Coupon rate = 1.79% , Price of stripped note = P = 95343.91, Period = 24 months

Face value = F = 100000

Since treasury note pays coupon semi-annually

Therefore half year coupon = C = (Coupon rate x par value)/2 = (1.79% x 100000)/2 = 1790/2 = 895

No of half year years = n = Months / 6 = 4 half years

Let y be 24 month zero coupon yield

then according the question

(1 + y/2)⁴ = 100895/95343.91

(1 + y/2)⁴ = 1.0582218

1 + y/2 = (1.0582218)^1/4

1 + y/2 = 1.014248

y/2 = 1.014248 - 1 = 0.014248

y = 2 x 0.014248 = 0.028496

y = 2.8496% = 2.850% (rounded to three places off decimal)