Question

3- Suppose that a two-year bond with a principal of $100 provides coupons at the rate of 6% per annum semiannually. Suppose that the zero-rates are

Maturity (years)	Zero Rate (%)
0.5	5.0
1.0	5.8
1.5	6.4
2.0	6.8

• What is the bond's yield to maturity expressed with the continuous compounding?

Answer choices:

6.76%, 5.3%, 6.54%,  7.05%. Please show how to do this exercise with a financial calculator

Please show how to do this

Answer 1

1) Calculate Continous Componding for 2 year Bond's price

Bond Continous Compond = P *

P is Principle / Cash flow per year = $100 * 6% = $6, for 0.5 year = $3, but 2nd year is $103 (Principle + Cost = $100 + $3),

R is Interest Rate, T is the Time of period / year,

So, 2 Year Continous Compond = 0.5 Year + 1.0 Year + 1.5 Years + 2 Years

= 3e^{-(5% * 0.5)} + 3e^{-(5.8% * 1.0)} + 3e^{-(6.4% * 1.5)} + 103e^{-(6.8 * 2.0)}

= 3 * 0.97531 + 3 * 0.94365 + 3 * 0.90846 + 103 * 0.87284

= 98.39 price of the bond

2) Using Yield Rate

We take Yield rate 6.76% from the Choice for example.

While applied the bond Yield rate its could match with the market price,

we use the r as 6.76% in the above Continous compounding calulation,

= 3e^{-(6.76% * 0.5)} + 3e^{-(6.76% * 1.0)} + 3e^{-(6.76% * 1.5)} + 103e^{-(6.76 * 2.0)}

= 3 * 0.9668 + 3 * 0.9346 + 3 * 0.9036 + 103 * 0.8735

= 98.39 same as the above price.