Please help me work out Discount to Yield

[Dopamine20]

Please could someone show me how to work out the discount to yield on the following. I am probably going wrong in the re-arranging of the equation:

£500,000 of 181 commercial paper is issued at £483,266.10. What is the discount to yield. The answer is supposed to be 7% - but I am looking for an explaination of how to arrive at this. Please help.

 

[Rhody Trader]

£500,000 received from £483,266.10 invested is a return of approximately 3.46%. Annualize that and you get close to 7%.

 

[Dopamine20]

Thanks for your answer. However, I am have trouble with the calculation to discover the annual rate i.e.7%. How do I work it out?

 

[A Dashing Blade]

(1+r/2)^2 =1.07
r = 500,000/483,266.10
Take into account that 2 should prolly be 360/181 or whatever your day count is.
That's pretty much all the fixed income maths you need.

 

[Dopamine20]

In the textbook it shows:

£483,266.10 = £500,000/1+r*181/365

gives

365*r*181 = 377.64

r = 377.64365/181 = 0.07


I can't figure this out - when I plug the numbers in I get 1.08

 

[A Dashing Blade]

500000/483266.1 = 1.0346267

360/181 = 1.98895

1.0346267 ^ 1.98895 = 1.0700489

where ^ = "to the power of"

 

[Dopamine20]

Thank you once again. It's just the way this was layed out in the text book was confusing, I just messed up the day count bit in the re-arrangement of the formula. Perhaps I should re-do GCSE maths! (Just for the record, it's 181/365 for UK Money Markets and simple interest calculation when <1yr.)