Hello everyone, According to the attached image, I want to ask why the rate of payment is 5,218,000.t instead of 5,218,000 only (without t). I think that the rate of payment is the derivative of the total payment received ( in this case, I believe that the total payment received is 5218000t ) Many thanks for any support.
I think they are asking the rate of payment at any time t during the first few years. Not necessarily the annual rate. £5218000 is the annual rate of payment. But if we need to find rate of payment for any time t Like- for t=1.5, then it will be £5218000×1.5 and so on for any value of t. So, the rate of payment will be £52,18,000t during the first few years. This is what I got.
I personally think that £52,18,000t should be the total payment during the first t years, not the rate of payment
The notes are correct here: £5,218,000t is the rate of payment at time t, not the total payment in the first t years. Consider the first year. Since the policies are sold evenly over each year, in the first year there are on average 5,000 policies paying premiums (as no policies have been sold at the start of the year and 10,000 have been sold by the end of the year). These will generate total income during the first year of 5,000*10*52.18 = £2,609,000. This corresponds to the answer we get if we integrate the stated rate of payment between the limits of 0 and 1.
Sorry, could you pleased explain me what "the policies are sold evenly over each year" mean and why there are on average 5,000 policies paying premium (i.e. why 5,000 ?? how could you calculate it) ? Thank you very much for your support.
