Annuity Due

An annuity due is a series of equal payments occurring at the beginning of each equal time interval, rather than at the end. Monthly rent paid on the first of the month for the month ahead is the textbook example: the tenant pays before using the space, not after, which places every cash flow one period earlier than it would fall under an ordinary annuity.

The distinction matters because shifting every payment forward by one period changes both the present and future value of the stream. An ordinary annuity, which pays at the end of each period, describes most loan repayments, bond coupons, and typical employee wages; an annuity due describes most lease and rent payments, insurance premiums paid at the start of coverage, and certain retirement income products. Because each payment under an annuity due arrives sooner, it is worth more today than the equivalent ordinary annuity, and because it has one extra period to earn interest before the series ends, its future value compounds to a larger amount as well.

Both present and future value of an annuity due can be calculated by first computing the ordinary annuity value and then multiplying by a factor of $(1 + i)$, where $i$ is the interest or discount rate per period — a simple adjustment that accounts for the one-period timing shift rather than requiring an entirely separate formula. This relationship is why financial calculators and spreadsheet functions typically include a setting to switch between “payments at end” and “payments at beginning” rather than requiring two unrelated calculations.

Lease accounting is the most common place accountants encounter annuity-due math directly, since lease payments are almost always due at the start of the rental period rather than the end, which affects how the present value of lease payments is calculated when recording a lease liability on the balance sheet. Certain retirement annuity products are also structured as annuities due when the insurer begins paying the retiree immediately upon purchase rather than after a waiting period, which changes the pricing the insurer offers compared with an equivalent ordinary annuity.

Because the difference between the two is sometimes just a single assumption buried inside a formula or calculator setting, it is one of the more common sources of small but consequential errors in lease valuation, loan amortization schedules, and retirement planning calculations; getting the timing assumption wrong understates or overstates the present value just enough to matter in a negotiated lease or financing arrangement, even though the underlying cash flows and interest rate are identical either way.

Paying $1,000 in rent at the start of each of the next five years, with a 6% discount rate, has a present value of roughly $4,465 — compared with about $4,212 if the same five $1,000 payments were instead due at the end of each year as an ordinary annuity. The gap, about $253, is exactly the extra value of receiving each payment one period sooner, which is the entire economic difference the annuity-due distinction captures.