Determine term structure of interest rates

Appreciate your help with this question.

You observe the following information on U.K. default-free government bonds. All
bonds pay annual coupons and have a par value of £100.
Price Maturity Coupon Rate
Bond A £96.266 2 years 2%
Bond B £103.885 2 years 6%
Using Bond A and Bond B what is the current term structure of interest rates?


£96.266 = \frac{£2.00}{1 + s_1} + \frac{£102.00}{\left(1 + s_2\right)^2}


£103.885 = \frac{£6.00}{1 + s_1} + \frac{£106.00}{\left(1 + s_2\right)^2}

for s_1 and s_2.

(Hint: multiply the first equation by 3 and subtract the second equation from it.)

I get s_1 = 2.0216\% and s_2 = 3.9995\%.

1 Like

Thanks for your reply.

By doing so I get 3.98% for the first bond and 3.94% for second bond. The question asks for term structure of interest rates, which means we are to derive the current 1-yr rate and 2-yr rate.

I don’t know what you mean by 3.98% for the first bond and 3.94% for the second.

Do you mean their YTMs?

If so, you didn’t follow what I wrote. I told you how to determine the 1-year spot rate and the 2-year spot rate, not the YTMs for the two bonds.

I got it now. Thanks so much for your response.

My pleasure.