The question is on page 21 and the answer is given on page 24 and 25. My question relates to the calculation at the bottom of page 24. In the formula given (89049.01 = 400 + (12X) * a..... + (12X) * 0.0035 * a.....), the expenses are included with the first and third terms on the right hand side. I am a bit confused here, shouldn't the expenses be added on the left hand side of the equation instead? As the premium should cover the expenses as well? "a......" denotes the annuity factor, sorry don't know how to type it out properly :-(
The classic CM1 equations is EPV(premiums) = EPV(benefits+expenses) ie the expected present value of the premiums paid by the policyholder should be sufficient to cover both the expected present of benefits as well as the expenses. So you're right that the premiums should cover the expenses but this means that we need to put the expenses on the right-hand side. For example, if the EPV of expenses went up by £200 then the EPV of premiums would also have to go up by £200 to offset. Does this help? Joe
Hi Joe, First of all, thanks a lot for helping out again here! The equation given by the answer (89049.01 = 400 + (12X) * a..... + (12X) * 0.0035 * a.....) is in the format: benefits = expenses + premium. So I think if we move the two expense terms on the right hand side to the left as they are right now (so without any sign change), we should arrive at the right answer. I definitely agree with the formula you gave EPV(premiums) = EPV(benefits+expenses), I just find the calculation’s wrong here.
Sorry, I'm not sure I follow (which could just be me). We work out the pot of money that the woman will use to buy the annuity as 89,049.01. This is the premium, which should cover both the benefits and the expenses. Both the benefits and expenses are positive values and depend on the level of annuity that the woman receives during retirement. The EPV of benefits are equal to 12X*a(12):61:<5> ie an annuity of monthly amount X payable for life (with a minimum of 5 years). The EPV of expenses is 400 + 12X*0.0035*a(12):61:<5> ie expenses are assumed to occur at a rate of 0.35% of the monthly annuity amount as long as the annuity is being paid. These are both outgoings for the insurance company. So we set the 89,049.01 equal to the expected present value of premiums + expenses and solve for X, to find out what level of annuity the woman can afford for her money. In other questions you may have had an unknown premium which you are looking to solve for. Here the unknown is the benefit amount, which affects the benefits (naturally) but also the level of expenses. Could this be the confusion? Joe
Sorry my sincere apologies, now I see how wrong I was, I took the maturity benefit as the real benefit here, but actually they are premiums. Sorry for wasting a lot of your time here and a lot of thanks for the very detailed answer and your patience with me. Can’t believe I was trapped in this question for a few hours
