A company has to make payments of £10,000 after 6 years and 8 years. The company wishes to immunise against small changes in interest rates and in order to do this purchases investments that provide payments of X after 5 years and Y after 10 years. Given that i = 5% (a) Show that Reddington’s first condition implies Xv5 + Y v10 = 14, 230.55 (b) Show that Reddington’s second condition implies 5Xv6 + 10Y v11 = 94, 209.59 (c) Hence calculate X and Y to the nearest pound. (d) confirm that Reddington’s third condition is satisfied.
This post has been moved to the correct forum as it CT1 and not CT7 (nor CT4). This is a very straightforward question from CT1 Chapter 14 Section 4 of the ActEd notes. Suggest you look there as it has a number of questions similar to this in the notes and the Q&A bank.
The easiest way to order them is by using our online store at: http://www.acted.co.uk/estore/ If you are based in India (as your name suggests) then you can get the CMP at a reduced rate (other products are not reduced). So select paper products from the left hand menu, then CT, then CT1. If your home address is based in India the discount will be applied automatically. Alternatively, you can send in an application form (also available on our website). Hope this helps.
John they are toooo expensive i have got my teachers notes but all it says in there is if a premium of £100 is charged. After 9 months the UPR would be 100 x 0.25 = £25 How do i use this to solve q2. If you could give me some hints not how to do the question. That would be soo great Thanks
I'm really sorry India but tutor's help is restricted to those who have purchased our materials and it would be unfair to provide "free" help to students who don't. It may be that a student may respond to your queries - though do note that the UK exam season has recently passed and so the number of students frequenting this site will be quiet until June.
never say never (a) Present value of liabilities equals present value of assets this is Reddington’s first condition and it implies that Xv5 + Y v10 = 14, 230.55 since , well firstly v = 1/ (1 + i) = 1/1.05 = 0.95238 L.H.S. of equation easy its just PV of assets X discounted for 5 years and Y discounted for 10 ie multiplying by v^5 and v^10 R.H.S. of equation is PV of liabilities so 10000 v^6 + 10000 v^8 and this is 10000(0.7462) + 10000(0.6768) = 14230.55, nearly,rounding error (b) This is to do with duration of liability 5Xv6 + 10Y v11 = 94, 209.59 notice the pattern here compared to (a) its like the derivative with respect to v except we increment the power of v one higher not lower { NOTE ; we are actually taking derivative with respect to i } L.H.S. again easy d/di of L.H.S. from (a) R.H.S. is 10000(6)v^7 + 10000(8)v^9 = 94209.59 42640 + 51568 = 94209 (c) easy just simultaneous equations 0.7835X + 0.6139Y = 14230.55 3.7310X + 5.8468Y = 94209.59 not going to bother working out but we need this answer for next part (d) well we have to take d/di on both sides of the equation so i claim that the equation is (5)(6)Xv^7 + (10)(11)Yv^12 = 10000(6)(7)v^8 + 10000(8)(9)v^10 so 30Xv^7 + 110Yv^12 = 726290 sub in with answers got in part (c) for X & Y to verify the 3rd conditions is met Well better late than never eh hope you maybe read this and its of help and i hope its right!
