Answer:
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
