the present value of a $2,000 face value zero-coupon 6-month bond is $1,941.75and that you
observe a yield curve with spot rates that increase 25 basis points for every six month increase in the term of a loanto set up an equation and solve for the spot rates corresponding to a term of 6 months and every 6 months after that (until the maturity of the bond we are pricing, which is 10 years in this case).
This question is actually from Finance 1.Oh dearie me. I seriously didn't think they threw you around this badly in Finance 1... Guess the moans of impossible Finance 1 exams are true then.
I think the problem was that I was trying to derive a formula for the present value of all the coupon payments and the bond, where it is best to use an excel spread sheet.Yep, definitely use an Excel spreadsheet (or some other computational tool) for this one. If the term of the bond was a lot shorter (2 or 3 years) you could be expected to do it with a scientific calculator I suppose. But good to hear you didn't actually have a problem in the first place!
Following this logic, does it make sense that for the second 6 months the return would be (6.0% + 0.25%)/2 = 3.125%, third 6 months it would be 3.25% and so on, when using these values to discount from the face value of the bond and each of the coupons?Yep, that looks good to me, i.e. the price is
Price = $4,176.6139 + $4,404.4889 = $8,581.1029. Does that seem to match with your formula?Yep, matches with what I got.
Thanks so much for your reply, and all your help! :)Haha, I didn't help all that much anyway, but no problem!