Date: Sun, 09 Jan 2005 10:57:14 +0000
From: Reestit Mutton 
Newsgroups: uk.finance
Subject: Level term assurance - how much to put aside to pay for it?

PLEASE NOTE: I am NOT qualified to give financial advice and this is in 
no way intended as advice to purchase level term assurance (for that, 
you should seek proper advice from a qualified IFA).

=======================================================================

I've been looking at taking out level term assurance and decided that 
(in my case, at least) it would be prudent to put enough money aside to 
pay for this in a separate account at the inception of this policy (as I 
can currently afford to do so) so that I need not worry about being able 
to pay for this throughout the term of the cover and therefore do not 
need to include cover for the premium payments themselves.

Anyway, being the mathematician that I am, I worked out an equation for 
calculating the necessary deposit up front that, along with an assumed 
rate of interest, and taking into account annual payments out of this 
account, will be sufficient for funding the policy on the basis that the 
premiums are guaranteed not to change throughout the term of the policy. 
For the benefit of the readers of this NG, here it is:

D = A(1 + (1+I) + (1+I)^2 + ... + (1+I)^(Y-1))/(1+I)^(Y-1)

where:
D = initial deposit
A = annual premium
I = assumed interest rate (net of tax), 0 < I < 1
Y = policy term (in years)

NOTE: While I firmly believe that the above equation is correct (and my 
annualised statement in the example below seems to corroborate this) 
feel free to point out any problems with it or ask any questions as to 
its derivation.

As an example, if you were to take out a 25 year policy that is charged 
at £100 per year and assume a fixed interest rate of 5%, reduced to 3% 
after tax at 40% (a conservative assumption), the calculation would be 
as follows:

D = initial deposit
A = 100
I = 0.03
Y = 25

Total premiums to pay = 2500.00

Initial deposit must be 1793.55

At end of year 1, balance = 1744.36
At end of year 2, balance = 1693.69
At end of year 3, balance = 1641.50
At end of year 4, balance = 1587.75
At end of year 5, balance = 1532.38
At end of year 6, balance = 1475.35
At end of year 7, balance = 1416.61
At end of year 8, balance = 1356.11
At end of year 9, balance = 1293.79
At end of year 10, balance = 1229.61
At end of year 11, balance = 1163.50
At end of year 12, balance = 1095.40
At end of year 13, balance = 1025.26
At end of year 14, balance =  953.02
At end of year 15, balance =  878.61
At end of year 16, balance =  801.97
At end of year 17, balance =  723.03
At end of year 18, balance =  641.72
At end of year 19, balance =  557.97
At end of year 20, balance =  471.71
At end of year 21, balance =  382.86
At end of year 22, balance =  291.35
At end of year 23, balance =  197.09
At end of year 24, balance =  100.00
At end of year 25, balance =   0.00

For anyone thinking of doing this, what I would suggest is that you do 
an annualised calculation as above and staple it to your paperwork. Then 
you can check your balance on account against the model every few years 
and, if it is deficient in any way (because of a period of particularly 
low interest rates) you only need to make up the difference in the 
feeder account to get back on track. Chances are, if your original 
interest rate estimate is conservative enough, you will never need to 
top the account up at any stage and may even end up with a sum of money 
remaining in the feeder account after the policy lapses.

If anyone uses Linux, I have written a simple perl program that does 
this calculation for you - PM me if you would like a copy.

HtH
Reestit Mutton
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