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Very struggling with the following problem: Let's suppose you buy a T- note. The trade day is Oct $2, 2020$. The note matures on Nov $15th 2021$ with a $5%$ coupon and yield to maturity $1.6%$. What is the clean price of the note, given face value of $100$?

The answer should be $103.73$

What I did so far: calculated accrued interest using

$\frac{100*8%}{2}$ * $\frac {days .since .the .previous .coupon}{total. days }$

I have calculated that days since the previous coupon was April $15th, 2020$. Is that the correct previous coupon date? I am having a trouble with calculating total days and days since previous coupon date.

Can you help me to calculate the accrued interest?

Day convention ACT/ ACT (actual to actual). Trade note settlement date is usually t + 1 business day.

Effective Learning
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  • Your header requests a dirty price, the body of the question requests a clean price. – lulu Dec 17 '20 at 15:59
  • Oh, thanks edited – Effective Learning Dec 17 '20 at 16:03
  • But if you want the clean price, why do you care about the accrued interest? – lulu Dec 17 '20 at 16:06
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    Side note; you should specify what day count convention you wish to apply here. This is a math site, you shouldn't suppose that everybody knows what day count applies to the coupons of Treasury notes. – lulu Dec 17 '20 at 16:06
  • @lulu because clean price = dirty price - accrued interest. So step 1 is to find the accrued interest, then the dirty price. I am having a problem with calculating the dates since the problem does not specify when was the last coupon date and how many days we have in total. – Effective Learning Dec 17 '20 at 16:32
  • Why is there and 8 in the numerator of your YTM calculation? It should be $\frac {\text{Days AI * CpnFace}}{\text{Days in Accrual Period2}}$ – Doug M Dec 17 '20 at 16:46
  • You should be aware that T-notes are typically semiannual, which makes the scheduled coupon dates obvious. Adjusting them (for weekends and holidays) is always a technical issue, of course. If you know how to compute the dirty price, then you should include that in your post. If you don't know how to do that, then knowing the compound interest won't help you. – lulu Dec 17 '20 at 16:47
  • Should stress: to compute the clean price you absolutely do not need accrued interest (that's kind of the point). You can just work with the forward part of the current coupon, and then, of course, the future coupon payments. – lulu Dec 17 '20 at 16:50
  • Coupons are paid May and November. Not April 15. – Doug M Dec 17 '20 at 16:53

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