Many insurers offer policies which provide a combination of insurance coverage up to a fixed retirement age and an annuity income after retirement. Premiums are normally payable until the retirement age is reached. The retirement income is often at the rate of $10 per month for each $1000 of face amount and is customarily payable for a fixed number of years certain and the remainder of life. Under normal circumstances the present value at the retirement age of the annuity income of $10 per month exceeds the face amount of $1000. This means that the policy must nature at the retirement age for an amount greater than the face amount, and that the policy reserves and cash values, in building up to the required maturi ty value, will also exceed the face amount for a period prior to retirement. Since it is impractical to have the face amount of insurance loss than the cash value, these policies provide that the death benefit will be equal to the cash value during the period when the cash value exceeds the face amount. Let 1 ~ k denote the present value at the retirement age, x ~ n, of the annuity to be provided at that age for each unit of face amount issued at age x. Then the policy can be regarded as a combination of a pure endowment of 1 ~ k due at the retirement age and a term insurance up to that age providing a death benefit equal to 1 or the total cash value on the policy whichever is greater. The net premium, P, for tho policy can therefore be written