Could you please explain this method with an example? I looked up some other threads for the explanation. I did not quite understand them. I only can understand that some excess premium is paid for extra sum assured opted for. I am pasting the text for your convenience. I would be grateful if you could throw some light especially on the font in bold Paid-up policy value plus premium for balance of sum assured This method cannot be used to calculate the terms for conversion to paid-up status. It involves the following three steps: (i) The policy is notionally converted to a paid-up policy at the alteration date. (ii) If the alteration involves a change in the outstanding term to maturity, the paid-up amount is converted to be appropriate to the new outstanding duration by the use of reversion factors, ie: Paid-up sum assured after change =Paid-up sum assured before change *Ax+t:n-t/Ax+t:m-t where n and m are the original and revised total terms respectively. (iii) A premium – calculated on the current premium basis – is then charged for the balance of the required sum assured over the – if need be, converted – paid-up policy amount. Meeting the principles The method produces acceptable results when applied to reduce the premium substantially, running into the paid-up value if the term is unchanged. It would be unlikely to reproduce the original premium if a policy is altered to itself. If the paid-up value is based on the surrender value, ie it is the latter thrown into reversion using the surrender value basis assumptions, then a reduction in the outstanding term to zero would produce the normal surrender value. However, if conversion to paid-up status is on some other basis then the method may well be inconsistent with the surrender value on a substantial reduction in outstanding term. It is not immediately obvious whether it meets the other principles.
Maybe a simple numerical example will help. A regular premium 20 year endowment has sum assured of 100,000. At time 5, the policyholder wants to change the sum assured to 120,000 keeping the term at 20 years. First we calculate the paid up sum assured, let's say this is 18,000. But the policyholder wants an extra 120,000 - 18,000 = 102,000 of cover. so we calculate the premium for a new 15 year policy with sum assured of 102,000. We'll use the same numerical example to look at the case where the term is changed. The original contract is a regular premium 20 year endowment with sum assured of 100,000. At time 5, the policyholder now wants to change the sum assured to 120,000 and reduce the term to 16 years. Again we calculate the paid up sum assured of 18,000. But this is for a policy with remaining term of 20 - 5 = 15. However, the policyholder wants a policy with remaining term of 16 - 5 = 11. So the insurer is not going to get so much interest on the policy and so a lower paid up sum assured should be offered. The new paid up sum assured is 18,000 * Ax+t:15 / Ax+t:11 = 12,000 say (we are saying that a sum assured of 12,000 in 11 year's time or earlier death, has the same present value of a sum assured of 18,000 in 15 years time). But the policyholder wants an extra 120,000 - 12,000 = 108,000 of cover. so we calculate the premium for a new 11 year policy with sum assured of 108,000. Looking at the penultimate point. Perhaps we calculate the paid up sum assured from the surrender value. So at time 5 perhaps the surrender value is 10,000. Then the 10,000 is used as a single premium to buy the new endowment with sum assured of 18,000, ie 10,000 = 18,000 Ax+5:15 (this is what we mean by thrown into reversion). We could then use the formula 10,000 = PUSA Ax+5:n to claculate the paid up sum assured for any term n. Clearly as n reduces to zero, the A factor increases to 1 and the PUSA tends to 10,000. This is what it means by saying a reduction in the outstanding term to zero would produce the normal surrender value. These alteration methods and their features are one of the hardest parts of the course to follow, but I hope these numerical examples help. Good luck in the exam. Mark
Thanks for the lucid explanation! The method produces acceptable results when applied to reduce the premium substantially, running into the paid-up value if the term is unchanged. So, does this principle say that if we start with a premium of zero and work our way backwards then we should get the paid up policy value (without altering the term)? It would be unlikely to reproduce the original premium if a policy is altered to itself. How so? Regards,
Yes, that's a good way of putting it. One reason is that the pricing basis may have changed. This method uses the current pricing basis to calculate the premium for the balance of the sum assured. So if the pricing basis has got stronger over time, the premium will go up if this method is used. Another reason is that the way in which the paid-up value is calculated may lead to problems, eg it may only be an approximation to the true value of the contract. Best wishes Mark
