Question

Find a 5-month forward price of a 5% coupon bond that matures 9 month from now if the face value of the bond is $1000; coupons are paid semi-annually; current price of the bond is $1000; and zero-rates for 3, 5, and 6 months are as follows: R356.5%; R5=6.7%; R6=6.8% Solution: I=25*exp(-0.065*3/12)=$24.597 F=(1000-24.597)*exp(0.067*5/12)=$1003.0166

Where is I= 25..., where 25 comes from?

I need a explanation for the first formula

Answer 1

The first formula is calculating the present value of the semiannual coupon payment. The semiannual coupon will be paid 3 months from now, since there are 9 months to maturity and the coupon is paid every 6 months.

Present value = future value * e^-rt,

where r = zero rate for 3 months. This is R₃ which is 6.5%, or 0.065.

t = time in years. This is 3 months, or (3/12) years.

future value = semiannual coupon payment = face value * coupon rate / 2 = $1000 * 5% / 2 = $25.

Present value = $25 * e^{-0.065*(3/12)}