Question

you are given the following spot rates: term 1 2 3 spot rate 5.00% s2 6.80% the annual effective yield of a 3-year bond sold at par with annual coupons is 6.75%. calculate s2.

Answer 1

The spot rate s2 is approximately 11.75%.

Step-by-step explanation:

The annual effective yield of a 3-year bond is 6.75%. To calculate s2, we can use the formula:

S2 = [(1 + r1)(1 + r2)]^(1/2) - 1

where r1 and r2 are the spot rates for the respective terms.

Given that the spot rates are 5.00% and 6.80% for term 1 and term 2 respectively, we can substitute the values into the formula to find s2.

S2 = [(1 + 0.05)(1 + 0.068)]^(1/2) - 1

Simplifying the expression:

S2 = (1.05)(1.068)^(1/2) - 1

S2 = 1.117545 - 1

S2 = 0.117545

Therefore, s2 is approximately 0.117545 or 11.75%.

Answer 2

The S2 among the table's spot rates is 6.59%

The 3-Year Par Bond is the bond that sells at its par value (basically bond price equals its par value), In this bond, the bond's yield (annual effective yield to maturity) equals its annual coupon rate.

Coupon rate of bond is 6.75 %.

Par Value = $ 1000 (assumed)

Bond Price = $ 1000

Annual Coupon = 0.0675 x 1000 = $ 67.5

Spot Rates: Year 1 = 5%, Year 2 = s2% and Year 3 = 6.8%

Therefore:

`1000 = 67.5 / (1.05) + 67.5 / (1+s2)^(2)+ 67.5 / (1.068)^(3) + 1000 / (1.068)^(3)\\1000 = 64.2857 + 67.5/(1+s2)^(2) + 876.303\\67.5 / (1+s2)^(2) = 59.4116\\(1+s2)^(2) = (67.5/59.4116)\\(1+s2)^(2) = 1.13614\\s2 = [(1.13614)^(1/2)] - 1\\s2 = 0.0659`

Therefore, the S2 among the table's spot rates is 6.59%