Annuity Due

An annuity due is a series of equal payments made at the beginning of equally spaced periods. Because every payment occurs one period earlier than in an otherwise identical ordinary annuity, an annuity due has a higher present value and future value when the periodic rate is positive.

The term describes payment timing, not a promise of investment performance and not necessarily an insurance product.

An annuity due moves every payment one period earlier. Each payment is discounted for one fewer period when finding present value and compounds for one additional period when finding future value.

Key Takeaways

• Annuity-due payments occur at the start of each period.
• The first payment normally occurs on the valuation date, at time 0.
• At a positive rate, the value equals the comparable ordinary-annuity value multiplied by (1+r).
• Rent paid in advance is a familiar timing example, although real rent may change and therefore may not be a level annuity.
• Exact payment dates, rate conventions, fees, and nonlevel cash flows must be checked separately.

Annuity Due vs. Ordinary Annuity

Assume there are (n) equal annual payments and the valuation date is time 0:

Both streams contain (n) payments. The annuity due starts immediately and finishes one period earlier; the ordinary annuity starts after one period and finishes at time (n).

Present Value Formula

First calculate the present value of the corresponding ordinary annuity, then move every payment one period earlier by multiplying by (1+r):

Where:

• (PV_{due}) is the value at time 0, when the first payment is due
• (PMT) is the equal payment each period
• (r) is the discount rate per payment period
• (n) is the number of payments

At time 0, the first payment is not discounted. The remaining payments are discounted according to how far in the future they occur.

Future Value Formula

The future value at time (n), one full period after the last beginning-of-period payment, is:

Every payment compounds for one period longer than the corresponding payment in an ordinary annuity. If (r=0), timing creates no interest effect and the value is simply (PMT \times n).

Worked Example: Beginning-of-Year Deposits

Assume $1,000 is deposited at the beginning of each year for five years and earns a constant 6% annual rate. The five deposits occur at times 0, 1, 2, 3, and 4, and the future value is measured at time 5.

For comparison, five $1,000 end-of-year deposits at the same rate have an ordinary-annuity future value of approximately $5,637.09. Beginning-of-year timing adds about $338.23 to the modeled value because each deposit compounds for one extra year.

The present value of the beginning-of-year stream is:

These figures assume a constant rate and no fees or taxes. They illustrate valuation mechanics rather than a guaranteed return.

Where This Timing Pattern Appears

An annuity-due pattern may describe:

• rent or lease payments required at the beginning of a period
• regular savings contributions made on the first day of each month
• service contracts paid in advance
• some insurance premiums or income payments
• certain retirement or benefit payments with advance timing

The label should be confirmed against the actual schedule. Payments that increase, depend on survival, skip dates, or include a final adjustment may require a different model.

How to Analyze an Annuity Due

1. Locate time 0. State the valuation date clearly.
2. Confirm the first payment date. If the first cash flow is immediate, beginning-of-period treatment may be appropriate.
3. Count payments, not just calendar labels. A five-year arrangement can have different payment counts depending on frequency and endpoints.
4. Match the rate to the period. Monthly cash flows require a monthly periodic rate.
5. State the future-value date. Specify whether value is measured on the last payment date or one period later.
6. Model exceptions separately. Add fees, residual values, irregular payments, taxes, and contingencies explicitly.

Common Mistakes and Limitations

Adding an extra payment

Shifting an ordinary annuity to time 0 does not increase the payment count. An annuity due still has (n) payments; all (n) are simply one period earlier.

Multiplying by (1+r) twice

If a calculator or spreadsheet function is already set to beginning-of-period mode, its output may already include the timing adjustment.

Assuming all advance payments are level

Rent often illustrates annuity-due timing, but rent increases, deposits, concessions, and irregular terms can prevent the full cash-flow stream from being a level annuity.

Ignoring product-specific risks

An insurance annuity may include guarantees, surrender charges, market exposure, fees, tax consequences, and insurer credit risk. The U.S. Securities and Exchange Commission’s Investor.gov annuity guide explains that costs, risks, and features vary by contract. The timing formula alone does not evaluate a product or determine suitability.

FAQs

Related Terms

• Future Value of an Annuity: The ending value of equal recurring payments.
• Present Value of an Annuity: The value of future recurring payments at an earlier date.
• Annuity Due Factor: The multiplier used to value beginning-of-period payments.
• Time Value of Money: The principle that makes payment timing financially significant.

This article is educational and does not provide personalized investment, tax, insurance, lending, or retirement advice.