# Thread: Interest rate (pa) of a zero-coupon bond

1. ## Interest rate (pa) of a zero-coupon bond

Hi,

I have this financial maths problem I cannot solve.

Supposing we have a bond, with a par value of $100, a coupon rate of 5.75% and it is selling for, 104.75. We solve for the yield to maturity using excel. The price of the bond was calculated using the settlement date of the 15th of September, 2009. It pays coupons on Jan 15 and July 15. It matures on January 15, 2010! If i want to work out the interest rate of a zero coupon bond, which is the equivalent, how do I do this? And also, if there is a second bond, that matures a year later, Jan 2011 how do i find the zero coupon interest rate for that. Thanks. 2. Originally Posted by Angel76 Hi, I have this financial maths problem I cannot solve. Supposing we have a bond, with a par value of$100, a coupon rate of 5.75% and it is selling for, 104.75. We solve for the yield to maturity using excel.

The price of the bond was calculated using the settlement date of the 15th of September, 2009. It pays coupons on Jan 15 and July 15. It matures on January 15, 2010!

If i want to work out the interest rate of a zero coupon bond, which is the equivalent, how do I do this?

And also, if there is a second bond, that matures a year later, Jan 2011 how do i find the zero coupon interest rate for that.

Thanks.
Angel,

Is the first bond redeemable at par value? Face value? What is the redemption price?

I deleted my post below as it did not account for the yield portion in the PV of coupons. I'm going to try to research this tonight and get you an answer.

3. Ok Angel, I got my act together and built you a lesson:

Go here --> Bond Yield Rate Formulas

This will solve for yield rate using the Yield Approximation Rate or the Bond Salesman's Method. I'd use the Yield Approximation Rate if I were you as that is more accurate. And disregard my last question, it's standard procedure to assume that redemption value is par if not stated as you did in your question. You'd still need to enter the redemption value as par though.

Your first bond only has a term of 4 months. You'd have to manually adjust your effective rate for periods less or more than your coupon payments.

So, if a coupon is payable semiannually, my yield rate calculates on a semi-annual basis.

Also, Kellison's book talks about Newton's Raphsons method which is what I think Excel does. If you want that built, let me know. The lesson I posted for you, if you lose this link for some reason, the lesson is searchable by any of the following keywords:

bond, yield, salesman, method, approximation

I hope this helps, let me know if you have questions.