Ordinary Annuity vs Annuity Due: A Simple Comparison

The key distinction in an ordinary annuity vs annuity due comparison is payment timing: an ordinary annuity pays at the end of each period, while an annuity due pays at the beginning. With the same payment, payment count, rate, and ending date, each annuity due payment earns one extra period of interest, so its future value is the ordinary annuity’s future value times (1 + the rate per period).

An annuity is a series of equal payments made at regular intervals. Moving every payment one period earlier gives each one an extra period of interest, so spotting the timing usually matters more than memorizing a second formula.

This lesson focuses on future value and assumes payments and compounding follow the same schedule. If you need the value today instead, jump to the present value section.

What is the difference between an ordinary annuity and an annuity due?

Both arrangements contain n payments. An annuity due does not add a payment; it shifts the same payment sequence one interval earlier.

Where you will see each one

These are common patterns, not rules, so always check the payment dates in the contract.

How can you tell which annuity you have?

Suppose a hypothetical plan runs from the beginning of Year 1 to the end of Year 4. Four ordinary-annuity deposits occur on December 31 of Years 1–4. Four annuity-due deposits occur on January 1 of Years 1–4. Both balances are measured at the end of Year 4.

“Starting today” usually signals an annuity due when today begins the first interval. “At each year-end” signals an ordinary annuity. Read the entire payment schedule: a word such as “annually” gives frequency but does not establish whether payments occur at the beginning or end.

Here is the same idea on a timeline, using four $2,400 deposits. Time 0 is today, and both balances are measured at time 4.

Exam tip: before you touch a formula, write the payment dates on a timeline and circle the valuation date.

How do you calculate the future value of an annuity due?

Let R be the equal payment, i the interest rate per interval, and n the payment count. First calculate the future value of an ordinary annuity. Then allow each payment one additional interval of growth.

The multiplier applies to the entire ordinary-annuity balance. Multiplying only the interest portion would omit the extra growth on the contributed principal. Also, simply replacing n with n + 1 in the ordinary-annuity formula adds one extra payment—a fifth payment in the Maple Design example. In the Maple Design example below, that shortcut gives $12,999.17, which is exactly one $2,400 payment too high. If you like that shortcut, subtract one payment at the end: $12,999.17 − $2,400 = $10,599.17.

Worked example: same deposits, different dates

Hypothetical example. Maple Design makes four deposits of $2,400 and earns 4% compounded annually. Compare payments at the end of each year with payments at the beginning of each year. Measure both accounts at the end of Year 4. Assume no opening balance, fees, withdrawals, or taxes.

The due balance is 4% greater before rounding. Each payment earns one extra year at 4%; the number and size of deposits remain unchanged. This is why payment timing changes future value even though both plans contribute the same $9,600.

Check the result payment by payment

For the annuity due, the four deposits grow for four, three, two, and one years. Thus $2,400 × (1.04⁴ + 1.04³ + 1.04² + 1.04) = $10,599.17. For the ordinary annuity, the exponents are three, two, one, and zero. Every exponent increases by exactly one.

A supplied ordinary-annuity factor table also works: locate the n-payment factor at the periodic rate, then multiply by 1 + i. Retain the available precision until the final answer. Do not add another 4% after already using an annuity-due factor.

Excel timing settings

Use =FV(4%,4,-2400,0,0) for ordinary payments and =FV(4%,4,-2400,0,1) for due payments. The last argument changes from zero to one. Keep the payment count at four. Microsoft’s FV documentation defines these timing settings and the cash-flow sign convention.

Does payment timing change present value too?

Yes. Present value is what a series of future payments is worth today. An annuity due has the higher present value at any positive rate because each payment arrives one period sooner and is discounted for one fewer period. The same multiplier works here too.

Using Maple Design’s numbers, four $2,400 payments at 4% have a present value factor of 3.629895.

In Excel, use =PV(4%,4,-2400,0,0) for ordinary payments and =PV(4%,4,-2400,0,1) for due payments. Microsoft’s PV documentation explains the same timing setting.

You will use this timing in lease accounting too. Under ASC 842, the FASB lease standard, a lessee measures the lease liability at the present value of lease payments not yet paid. So if the first payment is made on the day the lease starts, it is not part of the liability. It goes into the right-of-use asset instead, which is the lessee’s asset for its right to use the leased item. Deloitte’s lease accounting roadmap quotes this guidance.

Common ordinary annuity vs annuity due mistakes

Comparing different ending dates. The standard due formula measures value one interval after its final deposit. If a question asks for the balance immediately after that last beginning-of-period deposit, the valuation date is one period earlier. In the Maple Design example, that date is time 3 and the balance is $10,191.51, not $10,599.17. The last deposit has just been made, so it has earned nothing yet.

Using the annual rate for a half-year adjustment. At a 6% stated annual rate compounded semiannually, each half-year earns 3%, so the extra-period multiplier is 1.03, not 1.06.

Reversing the payment effect. For a fixed future goal, earlier deposits require a smaller payment. To reach $10,000 in four years at 4%, you would need $2,354.90 at each year-end, but only $2,264.33 at the start of each year. See how to solve future value annuity problems for the required deposit.

Key takeaways

• An ordinary annuity pays at the end of each period. An annuity due pays at the beginning.
• Both have the same number of payments. Only the timing moves.
• At the same ending date, future value of an annuity due = ordinary annuity future value × (1 + i), where i is the rate per period.
• The same multiplier works for present value.
• In Excel, the last argument is 0 for an ordinary annuity and 1 for an annuity due.
• Before you calculate, mark the payment dates and the valuation date on a timeline.

Want more practice? Try these future value annuity problems.

Three practice questions with answers

These questions are hypothetical. Assume constant rates, retained interest, and no fees or taxes.

1. Identify the payment type

A company makes four equal annual deposits, beginning today, and measures the balance four years from today. What type of annuity is this?

2. Calculate an annuity due

Three $900 payments occur at the beginning of each year. At 5% annual compounding, what is the balance at the end of Year 3?

3. Choose the correct multiplier

A six-payment ordinary annuity has a future value of $12,000 at 3% per half-year. What is the future value if each payment occurs one half-year earlier?

Frequently asked questions

Is the future value of an annuity due always higher?

It is higher for equal positive payments at a positive periodic rate when the payment count and final valuation date are the same. At a zero rate, both balances equal total contributions.

Does “due” mean the payment is overdue?

No. In this setting, annuity due means payment at the beginning of the period.

Do I need a separate annuity due table?

No. Use the ordinary-annuity future value factor for the stated payment count and rate, then multiply it by 1 + the periodic rate for the annuity due.

What are real-life examples of each type?

A typical mortgage or car loan is an ordinary annuity because the first payment comes after a period has passed. Monthly rent is an annuity due because you pay at the start of the month.

Is the present value of an annuity due also higher?

Yes, at a positive rate. Each payment arrives one period sooner, so it is discounted for one fewer period. Multiply the ordinary annuity’s present value by 1 + the periodic rate.

What do “in arrears” and “in advance” mean?

Payments in arrears come at the end of the period, which matches an ordinary annuity. Payments in advance come at the beginning, which matches an annuity due.

For more worked examples and practice, explore the Intermediate Accounting course.

About the author

Mansour Farhat, CPA, CIA, DBA, is the instructor behind Farhat Lectures.