ACCA BPP Chapter 8 Activity 3

Hello sir/maam, I have a question regarding a question on BPP F6 TX-UK Workbook regarding capital allowances. Here is the question: J&O Ltd purchased the following during year ended 31 March 2023 1 June 2022: Machinery £400,000 31 July 2022: Special Rate Expenditure £1,250,000 The TWDV of main pool at 1 April 2022 was £500,000 Calculate the maximum capital allowances for the year ended 31 March 2023 The answer key resulted in a total capital allowances of £1,735,000: Main Pool WDA £90,000 [£500,000*18%] FYA 130% £520,000 [£400,000*130%] AIA £1,000,000 FYA 50% 125,000 [(1,250,000-1,000,000)*50%] Meanwhile I found the total capital allowances of £1,742,500: Special Rate Pool WDA £7,500 [£125,000*6%] Main Pool WDA £90,000 [£500,000*18%] FYA 130% £520,000 [£400,000*130%] AIA £1,000,000 FYA 50% 125,000 [(1,250,000-1,000,000)*50%] Can you help me shed a light on why there is no writing down allowances on the special rate pool after applying the FYA and AIA, although there is a balance of £125,000 inside the special rate pool. Is this a rule? or an error made by the publisher of the book? Thank you in advance