Discounting is the core skill of valuation, and the present value of $1 table is its oldest tool. Every cell is a discount factor — the price today of a dollar paid at some point in the future. With a column of factors you can value bonds, compare payment offers, or work through a discounted-cash-flow problem by hand. This generator produces the table for the rates and periods you choose, to the precision you want.
How to generate the table
- Choose the first rate, last rate and step for the columns.
- Choose the first period and last period for the rows.
- Pick the number of decimal places.
The highlighted figure above the table is the bottom-right factor — the smallest in the grid, for the longest wait at the highest rate.
The discount factor formula
To discount any amount: PV = FV × PVIF(i, n).
Worked example
You are promised $12,000 in 10 years and could earn 6% a year elsewhere.
- Row 10, column 6%: 0.5584
- Present value: $12,000 × 0.5584 = $6,700.80 (with the unrounded factor 0.558395, $6,700.74)
So the promise is worth a little over $6,700 to you today. At 12% instead, the factor falls to 0.3220 and the value to about $3,864 — the same promise is worth far less to someone with better alternatives.
Discounting an uneven set of cash flows
Factors make multi-payment problems mechanical. Using an 8% column:
| Year | Cash flow | Factor at 8% | Present value |
|---|---|---|---|
| 1 | $2,000 | 0.9259 | $1,851.85 |
| 3 | $3,000 | 0.7938 | $2,381.50 |
| 6 | $5,000 | 0.6302 | $3,150.85 |
| Total | $7,384.20 |
This is exactly what the NPV calculator does, with an upfront cost subtracted.
Patterns worth noticing
- Halving points. At 6% a factor first drops below 0.5 at period 12 (0.4970); at 12%, at period 7 (0.4523). That is the rule of 72 in reverse.
- Long horizons shrink fast. At 10%, a dollar due in 30 years is worth about 5.7 cents today, which is why distant cash flows carry little weight in valuations.
- Columns sum to annuity factors. Adding a column from period 1 down to period n gives the matching entry in the present value of annuity table.
Getting rate and period to match
Tables are in periods. For semiannual bond coupons at a 6% annual yield, use the 3% column with twice as many rows as years. For monthly discounting at 6% a year, use 0.5% and months. The generator lets you create those fractional-rate columns directly instead of interpolating.
For single answers with any compounding, including continuous, use the present value of a future sum calculator. The reciprocal factors are in the future value table.
Factors are computed exactly and rounded to the decimals shown. For study and planning only; not financial advice.
Frequently asked questions
What is a present value of $1 table?
A grid of discount factors, 1 ÷ (1 + i)^n. Each cell tells you what $1 received after n periods is worth today at a rate of i per period. Multiply by any future amount to discount it.
How do I use the table to discount several cash flows?
Look up a factor for each cash flow's timing, multiply, and add the results. At 8%, $2,000 in year 1, $3,000 in year 3 and $5,000 in year 6 are worth 2,000 × 0.9259 + 3,000 × 0.7938 + 5,000 × 0.6302 ≈ $7,384 today.
Why do the factors get smaller down and to the right?
Down the table, the money arrives later; to the right, the discount rate is higher. Both mean you would need less money today to grow into $1 by the payment date.
How is the present value table related to the future value table?
Each discount factor is the reciprocal of the matching future value factor. At 6% for 10 periods, the future value factor is 1.7908 and the present value factor is 1 ÷ 1.7908 = 0.5584.
Can I add up a column to get annuity factors?
Yes. The sum of the factors for periods 1 through n in one column equals the present value of an annuity factor. At 5%, the first 20 factors add up to 12.4622.