The present value annuity factor answers a question that sits behind loans, pensions, leases and capital projects: what is a level series of future payments worth right now? Multiply the factor by the payment and you have the lump-sum equivalent. This generator produces the factor table for ordinary annuities (payments at the end of each period) or annuities due (payments at the start) over your own range of rates and periods.
How to generate the table
- Choose end of each period or start (annuity due).
- Set the interest rate range and step for the columns.
- Set the period range for the rows.
- Choose the decimal places.
Above the table, the result reads the bottom-right factor and shows its upper limit as the number of periods grows without bound.
The annuity factor formula
For an annuity due, multiply by (1 + i). The present value of a level payment is PV = PMT × factor.
Worked example
A piece of equipment will save $5,000 a year for 10 years. Your required return is 8%.
- Row 10, column 8%: 6.7101
- Present value of the savings: $5,000 × 6.7101 = $33,550.50
If the equipment costs less than about $33,550, it clears your 8% hurdle. If the savings arrived at the start of each year, the factor would be 7.2469 and the value about $36,234.
Using the table for loans and lump sums
| Question | Calculation |
|---|---|
| How much can I borrow at 8% for 10 years paying $5,000 a year? | $5,000 × 6.7101 = $33,550.50 |
| What is a 20-year, $10,000-a-year pension worth at 5%? | $10,000 × 12.4622 = $124,622 |
| What yearly payment repays $100,000 over 30 years at 6%? | $100,000 ÷ 13.7648 = $7,264.89 |
The last row divides instead of multiplying — that is the job of the annuity payment table, which lists the reciprocals directly.
Patterns in the table
- Diminishing returns to length. At 12%, going from 20 to 30 periods raises the factor only from 7.4694 to 8.0552, against a ceiling of 8.3333. Distant payments are worth little today.
- Row 1 equals the discount factor. One payment of $1 at the end of period 1 is worth 1 ÷ (1 + i).
- Columns are running sums. Each factor is the sum of the present value of $1 factors for periods 1 through n.
- At 0%, the factor equals n. Without discounting, $1 a period for 10 periods is simply $10.
Matching rates and periods
For monthly payments, use a monthly rate (annual ÷ 12) and the number of months. A 30-year mortgage at 6% uses the 0.5% column and row 360 — the generator handles both.
For exact values with growing payments, perpetuities or any compounding frequency, use the present value of annuity calculator. The accumulation side is in the future value of annuity table.
Factors are computed exactly and rounded to the decimals shown. For study and planning; not financial advice.
Frequently asked questions
What does a present value of annuity table show?
Each cell is the present value interest factor of an annuity (PVIFA): today's value of $1 received at the end of each of n periods, discounted at rate i. Multiply by a level payment to get the present value of that stream.
How do I use it to find a loan amount?
A loan's principal is the present value of its payments. If you can afford $5,000 a year for 10 years at 8%, you can borrow $5,000 × 6.7101 = $33,550.50.
What is the largest value a factor can reach?
As the number of periods grows, the factor approaches 1 ÷ i, the perpetuity factor. At 8% that ceiling is 12.5; at 12% it is 8.3333. Extra periods far in the future add very little value.
How is the annuity due factor different?
It equals the ordinary factor times (1 + i), because every payment arrives one period sooner. At 8% for 10 periods, 6.7101 becomes 7.2469. You can also get it by adding 1 to the ordinary factor for n − 1 periods.
How does this table relate to the annuity payment table?
They are reciprocals. Dividing 1 by a present value annuity factor gives the payment per $1 borrowed, the capital recovery factor. At 6% for 30 periods, 1 ÷ 13.7648 = 0.0726.