# Forward Rate Agreement

In the below question, “The bond has just paid a coupon and will make another coupon payment in 150 days”. Hence, shouldn’t we assume that the coupons are not semi-annual. They are paid every 150 days instead. And in such a case, each coupon will not be \$4. Any comments would be appreciated. Calculate the price of a 200-day forward contract on an 8% U.S. Treasury bond with a spot price of \$1,310. The bond has just paid a coupon and will make another coupon payment in 150 days. The annual risk-free rate is 5%. Answer is as follows: Coupon = (1,000 × 0.08) / 2 = \$40.00 Present value of coupon payment = \$40.00 / 1.05150/365 = \$39.21 Forward price on the fixed income security = (\$1,310 - \$39.21) × (1.05)200/365 = \$1,305.22

It is just telling you that the next payment is in 150 days and the current coupon is already paid, days ago or weeks ago, it doesn’t matter. It is semiannual.

Read again, it says “The bond has *just* paid a coupon”. Now tell me, if it just paid a coupon, then the next coupon (assuming they are paid semi-annually) should be in 180 days, right? And yeah, where exactly is it written that “It is semiannual.”? The question does NOT mention semi-annual, although one may decipher it going by the fact that it is a U.S. Treasury bond.

Trust me if it says “just paid…”, “just passed L2 exam”, it does not mean today. It’s just another way of saying it’s done and over. Semiannual is the default unless you’re told otherwise.