Method 2, uses both UDD and Woolhouse.

Fractional Ages

Because  is defined by a mortality table based on whole ages, it is necessary to obtain a value for  for integral 𝑥 and 0 ≤ 𝑡 ≤ 1 by assuming a uniform distribution of deaths (UDD) throughout the year of age 𝑥.

Payments more frequently that annually

For payments more frequently that annually, we use the Woolhouse method to calculate .

We have an 𝑚 times speed improvement over Method 1, because we need only calculate the present value of an annuity with annual payments and then make the (𝑚 – 1)/2𝑚 adjustment.