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

The Price of Bond today = $997.07

Explanation:

Semi annual coupons = $1000 * 5% / 2

Semi annual coupons = $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 bond today.  In case of continuous compounding, the formula for Present Value of any future Cash flow C is C*e^(-r*t).

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

Price of Bond = $25 * 2.71828^(-0.06*3/12) + 25*2.71828^(-.061*9/12)+ 1025*2.71828(-0.062*15/12)

Price of Bond = $ 25 * 2.71828 ^-0.015 + 25*2.71828^-0.04575 + 1025*2.71828^-0.0775

Price of Bond = $ 25 * 1/2.71828^0.015 + 25*1/2.71828^0.04575 + 1025*1/2.71828^0.0775

Price of Bond = $997.07

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