I got really confused on iv) part of this question. After going through the answer, I could not understand the part where the RPI's cancelled out. If the first 3 cancelled out, then why not 4th term? And after the terms cancelling out, I didn't get the part how the annuity for inflation is introduced. I appreciate any insight or information you can provide.
Hi Sudhan, To calculate the actual payments of the bond, we use inflation from 3 months before the issue date to 3 months before the payment. The last payment is at time 2 (end December2017), and the question introduction tells us that RPI 'until three months before it was sold' (ie end September 2017) was 2% per annum effective. When we then calculate the real value of those actual payments, however, we strip out inflation from the payment date back to the issue date, but without allowing for the 3 month lag. So for example,: when working out the real value of the 1st coupon (coupon at end June 2016) : we get the actual size of the payment by looking at inflation from end September 2015 to end March 2016 (so 6 months worth of 2% p.a.), and we then get the real value of that payment by stripping out inflation from end June 2016 to end December 2015 (so 6 months worth of 2% p.a.). As we have 6 months worth of 2% p.a. for each part of the calculation, it cancels out. when working out the real value of the 2nd coupon (coupon at end December 2016) : we get the actual size of the payment by looking at inflation from end September 2015 to end September 2016 (so 12 months worth of 2% p.a.), and we then get the real value of that payment by stripping out inflation from end December 2016 to end December 2015 (so 12 months worth of 2% p.a.). As we have 12 months worth of 2% p.a. for each part of the calculation, it cancels out. when working out the real value of the 3rd coupon (coupon at end June 2017) : we get the actual size of the payment by looking at inflation from end September 2015 to end March 2017 (so 18 months worth of 2% p.a.), and we then get the real value of that payment by stripping out inflation from end June 2017 to end December 2015 (so 18 months worth of 2% p.a.). As we have 18 months worth of 2% p.a. for each part of the calculation, it cancels out. when working out the real value of the 4th coupon (coupon at end December 2017) : we get the actual size of the payment by looking at inflation from end September 2015 to end September 2017 (so 24 months worth of 2% p.a.), and we then get the real value of that payment by stripping out inflation from end December 2017 to end December 2015 (so 24 months worth of y% p.a.). In the final bullet point, we know the inflation needed for the actual size of the payment, as we are given inflation information in the question until end September 2017. However we don't know the inflation for the real value of the payment, as that also needs to include inflation for the final 3 months (the 3 months from September 2017), which the question does not give. More specifically, the inflation for the real value of the final payment needs to be inflation over the 2 year period between end December 2015 and end December 2017. We do know inflation for the first 21 months (or 1.75 years) of this period (2% p.a. effective, or compounded to be 1.02^1.175), but we don't know inflation for the last 3 months (let's call it x% p.a., or compounded to be (1+x)^0.25. Hopefully this helps with your question about the terms cancelling out and allows you to make more sense of the rest of the solution, but do let me know if you have any further questions. Richie
