Question

3. A 2-year T-note was issued 9 months ago with a face value of $1000. It pays a 5% per annum coupon, paid semiannually. Suppose that the 3-month zero rate is 6%; the 9-month zero rate is 6.1%; the 15-month zero rate is 6.2%; and the 21-month zero rate is 6.3%, where all of these rates are per annum with continuous compounding. What is the price for the bond today?

Answer 1

The semi annual coupons are = $1000 *5%/2 = $25.
As 9 months is already over in the two year bond, the coupons are payable :
3 months from now, 9 months from now and 15 months from now.

The present value of all these coupons and the principal should be equal to the price of the bind today.
In case of continuous compounging, PV of any future Cashflow C is C*e^(-r*t). We will use the formulae.

Thus,

Price of Bond = $ 25 * e^(-0.06*3/12) + 25*e^(-.061*9/12)+ 1025*e(-0.062*15/12)

Using the value of e as 2.71828 we get,

Price of Bond = $997.07 (Ans)

Ans : The price of the bond is $ 997.07