Question about Automatical Premium Loan

[eriksong]

my manager asked me to provide a formula of remaining coverage days calculation related to APL.
The background is that one insured did not pay his premium on time, after 60 days grace period, all of the Account Value (or Cash Value) started to be used to pay his premium.
My question is that how do I calculate the remaining coverage days based on its account value.
I guess it is better for me to put a real problem here.

a policy issue date is 2011-2-20, the gross premium is 20000 annually,after the 1st premium payment, the insured did not make the 2nd payment on 2012-2-20. After 60 days grace period, APL started.

At the end of first policy year, the CSV(1) = 10240, assume the insured made the 2nd payment of 20000, the CSV(2) would be =23340.

the other assumption is the loan interest rate is 6.1% annually,the expense&comission loading for the 2nd policy year is 12%.


How do I calculate the remaining coverage days until the account cash value is not enough to pay even one day's premium!

Please help me out....Thanks in advance

[Gandalf]

You need to look at the policy and decide how it works. The answer may be different for diffeent companies.

Let me change your example slightly. Instead of assuming that the cash value right if the 20,000 premium was paid would be 23340, suppose it would be 19,340. In that case he could not borrow 20,000. What would the policy say happens? Among the possibilities are:
1. He cannot pay by APL. An alternative procedure (perhaps extended term insurance) applies.
2. The premium mode changes to something shorter (perhaps monthly) and the monthly premium is paid by APL.
Which one of those - or what other alternative - applies at your company? We don't know.

Another important question. You said the policy's cash value would become 23,340. If he had paid the premium, and had that cash value, what is the loan value, the maximum amount he could borrow? Probably less than 23,340, because the loan value would likely include some future interest. (Probably more than 20,000 also, so that this time he could pay the entire premium by APL).

Basically, I think you need to project the loan and cash value and loan value forward, a year at a time, until he cannot borrow the annual premium at the start of a year. Then, if your policy provides for change of premium mode, change the premium mode and start projecting modally.

Eventually he cannot pay even one modal premium by APL, then calculate his coverage situation under whatever other provision applies.

Procedure may be different depending on how your APL provision operates.

[FattyMcGee]

quick estimate:

CSV(1) = 10,240
CSV(2) = 23,340

linear interpolation of CSV
CSV(1.2) [1 year, 2 months] = 12,423.33

At t = 1.2, can use all of CSV to pay premium.

% Prem Paid = (12,423.33 / 20,000) = 0.6211

Covered days = 0.6211 * 365 = 226.7, round to 227.

Already covered 60 days in grace period.

Remaining days of coverage: 227 - 60 = 167.


This is just an example, and would be contingent upon:
CSV interpolation
All of CSV can be used to pay premium with loan provision for extended term
Coverage proportion does not change for extended term period

Again, as Gandalf said, you need to know what the provisions in the contract are, and apply them to the amounts available. If you have more specifics we may be able to help again, but until then we're just throwing snot at the wall to see what sticks.

[eriksong]

Thank you for the help
As I know, the Provision said that if the insured can not pay the premium on the payable day, we give him 60 days grace period. If the insured choose APL option when he signed policy, once the grace period ends, we take his account value at the payable day which the insured does not make the payment, in my example, the account value is 10240, and this amount is the maximum loan amount which insured could borrow.

once we have the loan amount, we see if this amount could be enough to pay one term premium. In above case, 10240 is less than 20000(annual premium), therefore, we change the premium mode to daily premium payment, with 6.1% annual loan interest, in order to calculate the days the insured can be covered.

What makes me confused here is that as time goes by, the daily premium would be paid by loan, then the cash value would also changes, which implied that the insured could use some more money to pay the premium

My calculation is as follows
loan amount =10240
daily premium = 20000/365 = 54.8
Remaining Days(1) = 10240/54.8 = 186.86 days = 186 days
so 186 days after 2012 - 2- 20, the date would be =2012 - 5 -16

CSV(2012-5-16) = CSV(1) * ( 365-186)/365 + CSV(2)*186/365
= 10240 * 0.49041 + 23340 * 0.50959
= 16915.6

with 6.1% annual interest, daily interest = 6.1%/365 = 0.01671

at 2012-5-16, I calculate the remaining days at this point use the same method

Remaining Days (2) = ( 16915.6 - 54.8*(1+0.01671)*186 )/54.8 = 119.57 =119 days

I would continuously do this several time until the final cash value < 54. 8, then I would add all the Remaining Days(x) together = 186+119+.......
the coverage days would be greater than 365, which means with this 10240 loan amount, the insured could get another 1 full year to be covered....

I thought that my method was reasonable, but the result made me confused....

[Gandalf]

I think one major problem is that you should just allow him to borrow the 20,000 to pay the premium.

As I understand your facts, this combination of transactions is possible: he pays the premium of $20,000 by check, then requests a policy loan of $20,000. You would conclude he has sufficient loan value, and you would send him the $20,000. Net effect: 0 cash changed hands, and his policy would be inforce for the full year.

Under those facts, you should allow him to pay the annual premium of 20,000 by APL, because it leads to exactly the same place: no cash changed hands, the premium has been recorded as paid, there is a loan of 20,000.

So it doesn't surprise me that the coverage calculated the other way would go beyond a full year.