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Finance question help

RichieZ

RichieZ

Diamond Member
A zero-coupon bond with six months to maturity currently has a yield-to-maturity of 3% per annum with continuous compounding. A zero-coupon bond with twelve months to maturity currently has yield-to-maturity of 4% per annum with continuous compounding. A one-year bond with a face value of $1000 and semiannual coupons has a coupon rate of 5% per annum with semiannual compounding. Assuming there are no arbitrage opportunities (all bonds are priced fairly relative to each other). What should be the price of the coupon-paying bond?

How do i discount the coupon bond? I'm not sure but i think it would be:

PV = 25/e^.015 + 1025/e^.04

i'm kinda stumped, this is on a practice test w/o answers. Help pls!
 
Well, if I'm reading this right, you shouldn't worry about the continuous compounding, as the one-year bond has semi-annual compounding. Should just be something like PV = 25/(1+.015) + 1025/(1+.02)^2.

I could be wrong, I'm very, very tired right now.
 
Originally posted by: Orsorum
Well, if I'm reading this right, you shouldn't worry about the continuous compounding, as the one-year bond has semi-annual compounding. Should just be something like PV = 25/(1+.015) + 1025/(1+.02)^2.

I could be wrong, I'm very, very tired right now.
Click to expand...

whoops you are correct i meant to write it out like that. I just wasn't sure if I used the right interest rates?

So I can infer the interest rate from the zero-coupon bonds right? The face value and the secound coupon should be discounted at 2% and the first coupon should be discounted at 1.5% yes?
 
Originally posted by: RichieZ
Originally posted by: Orsorum
Well, if I'm reading this right, you shouldn't worry about the continuous compounding, as the one-year bond has semi-annual compounding. Should just be something like PV = 25/(1+.015) + 1025/(1+.02)^2.

I could be wrong, I'm very, very tired right now.
Click to expand...

whoops you are correct i meant to write it out like that. I just wasn't sure if I used the right interest rates?

So I can infer the interest rate from the zero-coupon bonds right? The face value and the secound coupon should be discounted at 2% and the first coupon should be discounted at 1.5% yes?
Click to expand...

I think the rate they quoted was the annual rate, so to convert it to semi-annual compounding you just divide by two. And, yes, you're correct.
 
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