# Calculating spot rate of interest

You are given the following information regarding the domestic government fixed-interest bond market:

• The current price of a one-year bond paying coupons at a rate of $4.5$% per annum and redeemed at par is £100.41 per £100 nominal
• The current price of a two-year bond paying coupons at a rate of $6.5$% per annum and redeemed at par is £100.48 per £100 nominal

Calculate the two-year spot rate of interest, $y_2$

I'm not sure how to start this question. Do we have to work out the first and second year forward rates?

• Is this a homework assignment? You posted a similar plea on Math.SE. – chrisaycock Apr 18 '13 at 19:23
• It's a practice question in one of the tutorial sheets, not a homework assignment. They have only given the answer of the question but I do not know how to solve it. – neverloggedin Apr 18 '13 at 22:13

The one year annual spot rate r1: $$1.045/(1+r1)=1.0041 => r1 \approx 4.0733\%$$ The one-two year forward rate r1,2: $$.065/(1+r1)+1.065/(1+r1)(1+r1,2)=1.0048 => r1,2 \approx 8.5927\%$$ The two year spot rate r2= $$(1+r2)^{2}=(1+r1)(1+r1,2) => r2 \approx 6.3090\%$$