Present Value of an Annuity Due: Formula and Examples

The present value of an annuity due is what a series of equal payments, made at the start of each period, is worth today. Calculate it by multiplying the ordinary annuity present value by (1 + i). Four $3,200 yearly payments at 6%, starting today, are worth $11,753.64.

Discounting means shrinking a future payment to what it is worth today. Moving every payment one period earlier removes one discounting period from each cash flow. For identical positive payments at a positive rate, an annuity due therefore has a higher present value than an ordinary annuity. So check the payment date first in any annuity problem.

What changes when payments begin today?

Assume the valuation date, meaning the moment you are measuring value, is today, or time 0. Four ordinary-annuity payments occur at times 1, 2, 3, and 4. Four annuity-due payments occur at times 0, 1, 2, and 3. The payment count stays four. Only the timing changes.

The phrase “annually” specifies frequency but does not identify beginning or end timing. Read the actual payment dates. A payment due today needs no discount: its present value equals its face amount.

What are examples of an annuity due?

An annuity due is any series of equal payments that starts at the beginning of a period. Common examples include rent paid on the first of the month, lease payments due at signing, and insurance premiums paid in advance.

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

Let R be one payment, i the interest rate per payment interval, and n the number of payments. For a nonzero rate, first calculate the ordinary-annuity present value, then adjust for earlier payments:

In plain text, that is PV = R × ((1 − (1 + i)^(−n)) ÷ i) × (1 + i).

Alternatively, separate the payment today from the remaining n − 1 ordinary payments:

These approaches value the same cash flows. The California State Board of Equalization’s annuity timing lesson confirms the factor conversion. If a table already supplies an annuity-due factor, use it directly. Multiplying that factor by 1 + i again would count the timing advantage twice.

Annuity-due factors at common rates

Multiply one payment by the factor below to get the present value. Each factor assumes payments at the start of each period.

Rounding note: The table factors are rounded to five decimal places. The worked examples use greater precision, so small rounding differences can occur. For example, $3,200 × 3.67301 = $11,753.63, while the full-precision calculation gives $11,753.64. Keep full precision during calculations and round the final dollar amount to cents.

Original example: four beginning-of-year payments

Hypothetical example. Harbor Training agrees to four annual payments of $3,200 for equipment use. The first is due today, followed by payments one, two, and three years from today. Assume a 6% annual discount rate. Find the value of all four payments immediately before the first payment.

The otherwise identical ordinary annuity would be worth $11,088.34. Earlier payments increase present value by $665.30. The difference equals 6% of the unrounded ordinary-annuity value.

As an independent check, add $3,200 today to the present value of three $3,200 year-end payments. In Excel, use =PV(6%,4,-3200,0,1). Microsoft’s PV documentation identifies type 1 as beginning-of-period timing.

Worked example: monthly rent paid in advance

Hypothetical example. A tenant pays $1,500 at the start of each month for 12 months. The annual rate is 12%, compounded monthly. Because the payments are monthly, use the monthly rate: i = 1% and n = 12.

Here is a quick check. The first $1,500 is due today, and the other 11 payments are worth $1,500 × 10.367628. Together, they total $17,051.44.

In Excel, use =PV(1%,12,-1500,0,1).

How do you calculate it in Excel or on a financial calculator?

Excel’s PV function uses this pattern: =PV(rate, nper, pmt, fv, type). Rate is the rate per period, nper is the number of payments, and pmt is the payment. The fv argument is the future value, or additional ending balance. Use 0 when there is no additional ending balance, as in these examples. Set type to 1 for beginning-of-period payments. Enter the payment as a negative number so the answer comes back positive.

For Harbor, =PV(6%,4,-3200,0,1) returns $11,753.64.

On a financial calculator, switch to begin mode, often labeled BGN, before you solve. Then switch back to end mode so your next problem is not thrown off.

How do you compare an annuity due with other payment options?

Present value allows an immediate cash amount and a payment stream to be compared consistently. Keep the service period, benefits, and relevant cash flows comparable before choosing the lower present-value cost.

Hypothetical extension. Assume Harbor can obtain equivalent four-year benefits in three ways. All other costs, risks, and taxes are identical, and any purchased equipment has zero residual value after four years. Use the same 6% rate.

Alternative A has the lowest cost under these assumptions. Its receipts reduce cost and use an ordinary-annuity factor; Alternative B’s payments use a due factor. This is a cash-flow comparison, not a determination of lease classification or a journal entry under an accounting standard.

How does an annuity due connect to lease accounting?

Under ASC 842, the lease standard from the Financial Accounting Standards Board (FASB), a lessee measures the lease liability at the present value of lease payments not yet paid (ASC 842-20-30-1). A lessee is the party renting the asset. A payment made at or before the start of the lease is not in that liability. Instead, it goes into the right-of-use (ROU) asset, which represents the right to use the leased item (ASC 842-20-30-5).

Here is how that works for Harbor. Assume the four $3,200 payments are lease payments, the lease rate is 6%, the lease starts today, and there are no other lease costs or incentives.

Exam tip: payments actually made at or before lease commencement are excluded from the lease liability. A payment that is merely due at signing but remains unpaid is still included. That is why the value after the first payment matters. You can read more in Deloitte’s guide to ASC 842 lessee measurement

What are the most common annuity due mistakes?

• Adding an extra payment. Shifting four payments earlier does not create a fifth payment.
• Discounting today’s payment. The first due payment is already at the valuation date.
• Using the wrong rate. With 6% nominal annual interest compounded semiannually and half-year payments, the conversion multiplier is 1.03.
• Adjusting twice. An annuity-due factor already includes the timing shift, so do not multiply it by 1 + i again.

Confusing before and after payment. Harbor’s $11,753.64 includes the $3,200 due today. Immediately after that payment, the remaining payments have a value of $8,553.64. So always state the exact moment you are valuing. To find a payment amount from a known present value, see solving present value annuity problems.

Key takeaways

• An annuity due pays at the start of each period, so the first payment is not discounted.
• Multiply the ordinary annuity present value by (1 + i) to get the annuity due value.
• You can also add one payment to the value of the remaining n − 1 ordinary payments.
• In Excel, set the PV function’s type argument to 1.
• If you already have an annuity-due factor, use it directly.

Three practice questions with answers

These original questions are hypothetical and assume constant rates.

1. Identify the discount periods

Five equal annual payments begin today. How many years is the final payment discounted when finding value today?

2. Calculate a due value

Find the value of three $1,200 payments at the beginning of each year, using 4% annually.

3. Use the factor supplied

A question provides an annuity-due factor of 4.54595 (five payments at 5%) and a payment of $900. Should you apply another 1 + i adjustment?

Frequently asked questions

Is an annuity due always worth more?

An annuity due has a higher present value than an ordinary annuity when both have identical positive payments, the rate is positive, and you measure them on the same date. At zero interest, both values equal total payments.

Does an annuity due have fewer payments?

No. An annuity due has the same number of payments as the matching ordinary annuity. Each payment is simply discounted for one fewer period.

Can I use an ordinary-annuity table?

Yes. Multiply the ordinary-annuity factor for n payments by 1 + i, or add 1 to the ordinary-annuity factor for n − 1 payments.

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

An annuity due pays at the start of each period, and an ordinary annuity pays at the end. The payment count is the same, but the annuity due is discounted one period less.

Is rent an annuity due?

Yes, when it is paid at the start of each period. Rent due on the first of each month for that month is a common example.

What rate do I use with monthly payments?

Use the rate for one payment interval. A 12% annual rate compounded monthly gives i = 1%, and n counts months.

How do I calculate an annuity due in Excel?

Use the PV function with 1 as the type argument. For example, =PV(6%,4,-3200,0,1) returns $11,753.64.

Want more practice with annuities and bonds? Explore the Intermediate Accounting course, or start with the free sample course.

About the author

Mansour Farhat, CPA, CIA, DBA, teaches accounting and exam topics at Farhat Lectures, with lessons for CPA, CMA, and EA candidates and accounting students.