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Is it possible to buy term life insurance whose payoff varies with time e.g. as in:

$E = (1-\frac{x}{T})(1+r)^x$ where,
T = term of policy
r = rate of inflation (e.g., 0.03)
x = time when policy holder dies

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Mortgage life insurance policies sold by some companies have the amount insured reduce approximately as the balance still owing on the mortgage reduces: very slowly in the earlier years and accelerating in later years. You can get them for 15, 20, 25, 30 year mortgages. I don't think this is quite what you want since you seem to want the payout to reduce linearly (ignoring the inflation factor for now) with each year. – Dilip Sarwate Jan 16 at 20:31

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Google for "decreasing term life insurance" and choose from the many hits there. Most pages say

A big portion of the decreasing term insurance found today is in the form of mortgage life insurance, which pegs its benefit to the remaining mortgage on the insured' home.

which supports what I said in my comment on your question.

If you are absolutely sure that the inflation rate will remain r over the term of the policy, and are adamant that the payoff be exactly what your formula says, you may be out of luck. Else I am sure that many companies will tailor a policy that meets your requirements quite closely even if they fail to match the requirements perfectly.

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