PVIFA Table

The table below displays present value interest factors of annuity (PVIFA) for 1 to 25 periods at discount rates spanning 1% to 20%. Each factor represents the combined present worth of receiving $1 at the end of every period for the given horizon. To value any stream of equal payments, find the appropriate row and column and multiply the factor by the payment size.

PVIFA Table: 1%-20%, 1-25 Periods

What Is PVIFA?

The present value interest factor of annuity (PVIFA) tells you the current worth of a series of $1 payments received at the end of each period for $n$ periods, discounted at a constant rate $r$. It collapses multiple discounting steps into a single multiplier:

Where $r$ is the per-period discount rate (expressed as a decimal) and $n$ is the total number of payment periods. To find the present value of any ordinary annuity:

For example, a 15-year annuity paying $1,000 per year discounted at 8% has PVIFA = 8.5595. The present value is $1,000 × 8.5595 = $8,559.50.

How to Read the Table

1. Count the payment periods - this determines your row ($n$).
2. Identify the per-period discount rate - this determines your column.
3. Look up the factor at the intersection of row and column.
4. Multiply the factor by the periodic payment amount to obtain the annuity's present value.

Worked Example

You are evaluating a lease that requires 10 annual payments of $4,000 each. Your required rate of return is 6%:

• Row: $n = 10$
• Column: 6%
• PVIFA: 7.3601
• Present value: $4,000 × 7.3601 = $29,440.40

This tells you that the entire stream of lease payments is equivalent to a single lump-sum of $29,440.40 paid today.

Observations from the Table

When n = 1, PVIFA Matches PVIF

When there is only one payment, the annuity factor reduces to the single-payment discount factor. Compare the first row here with the first row of the PVIF table - the values are identical. With just one cash flow to discount, there is no summation effect.

Factors Increase with Each Additional Period, but by Shrinking Increments

Each new row adds one more discounted payment, so PVIFA always grows as $n$ increases. However, the marginal contribution of each successive payment gets smaller because it is discounted more heavily. At 10%, the jump from $n = 1$ to $n = 2$ adds 0.8264, while the jump from $n = 24$ to $n = 25$ adds only 0.0923.

High Discount Rates Push the Factor Toward a Ceiling

At steeper rates, distant payments contribute almost nothing. The theoretical upper limit of PVIFA as $n$ approaches infinity is $1 / r$ - the so-called perpetuity factor. At 20%, that ceiling is 5.0000, and the table shows the 25-period factor at 4.9476, already within 1% of the maximum. At 1%, the ceiling is 100.0000, so even 25 periods captures barely a fifth of it.

Lower Rates Yield Much Larger Annuity Values

Compare the 25-period factors: at 1% the PVIFA is 22.0232, while at 20% it is just 4.9476. Cutting the discount rate dramatically raises how much a payment stream is worth today, because each individual payment retains more of its face value after discounting.

The Rate Must Match the Payment Frequency

The table presumes that the discount rate and the period length refer to the same time interval. If you receive monthly payments but have an annual discount rate of 9%, convert to a monthly rate of 0.75% and use $n$ in months. Rates like 0.75% are not among the listed columns, so the PVIFA Calculator handles those cases more conveniently.

Ordinary Annuity vs. Annuity Due

Every value in this table applies to an ordinary annuity - payments arrive at the end of each period. If payments instead occur at the beginning (an annuity due), each one is discounted one period less. The adjustment is straightforward:

For instance, at 6% and $n = 10$, the ordinary-annuity factor is 7.3601. For an annuity due: 7.3601 × 1.06 = 7.8017.

How PVIFA Relates to the Other Factor Tables

PVIFA rounds out the set of four time-value-of-money factors. Each handles a different cash-flow pattern:

Mathematically, PVIFA is the running total of PVIF values from period 1 through $n$. It can also be expressed through FVIF:

And the link to FVIFA is:

So with any one of the other three tables on hand, you can derive every PVIFA entry without memorizing a separate formula.

Frequently Asked Questions

What everyday problems does PVIFA solve?

Anytime you need to price a fixed stream of cash flows - mortgage affordability, bond valuation, lease-versus-buy analysis, pension fund obligations, or lawsuit settlement comparisons - PVIFA gives you the multiplier that converts the periodic payment into a single present-day figure.

How do I handle a discount rate not shown in the table?

For a quick estimate, interpolate between the two bracketing columns. For precision, use the formula $(1 - (1 + r)^{-n}) / r$ or the PVIFA Calculator.

Can I use this table for monthly payments?

Absolutely. The table is agnostic about the calendar unit - "period" can mean a month, a quarter, or a year. Just make sure the discount rate reflects the same interval. A 12% annual rate with monthly payments becomes a 1% monthly rate; read the 1% column with $n$ equal to the number of months.

Why does PVIFA level off at high discount rates?

Because distant payments are discounted so aggressively that they add almost nothing. At a 20% rate, a payment arriving in period 25 carries a discount factor of roughly 0.0105 - barely one cent per dollar. Adding more periods beyond that barely moves the total. The mathematical limit is the perpetuity formula $1 / r$, which at 20% equals 5.

When should I use PVIFA instead of PVIF?

Use PVIF when discounting a single future amount - one payment at one point in time. Use PVIFA when discounting a series of identical payments spread over multiple periods. If the payment amounts vary from period to period, you will need to discount each one individually with PVIF and sum the results.