If the frequency of payments is more than 1 per year, an approximation method is necessary because mortality tables are constructed with rates only at whole ages. For an annuity with payments made 𝑚 times per year, the present value formula is:

and by making the simplifying assumption that 𝑣𝑡𝑡𝑝𝑥 is linear function of 𝑡 for 0 ≤ 𝑡 ≤ 1, then it can be shown that

where 𝑥 is not necessarily a whole number. The is the so-called "Woolhouse method" or the  shortcut. A proof of this shortcut is provided.