An annuity in advance is another name for an annuity due, a series of equal payments made at the beginning of each period rather than at the end. Rent paid on the first of each month for the month ahead is the standard example. The main entry explains how the valuation differs and gives a worked example.
Where the term is used
"In advance" is the usual phrasing in actuarial work, insurance and British and Commonwealth textbooks, where payment timing is described as either in advance or in arrears. Finance and accounting texts in the United States more often say annuity due. The opposite case, with payments at the end of each period, is called an ordinary annuity or an annuity in arrears.
The difference matters for valuation. Because each payment of an annuity in advance arrives one period earlier, it has more time to earn interest and is discounted for one period less. Its present value and future value are therefore equal to those of the matching ordinary annuity multiplied by one plus the periodic interest rate.
Common examples include insurance premiums paid at the start of each cover period, savings plans with deposits made on the first day of each month and lease payments due at the start of each rental period. Using the wrong timing assumption in a calculator or spreadsheet is a frequent source of small errors in loan, lease and retirement calculations.