Present Value Calculator
Find what a future sum, a stream of equal payments or a payment that never ends is worth today. Choose the kind of cash flow, enter the payment, the discount rate and the time, and see the present value with the formula worked out and a discount factor table. Free, no sign-up.
Your numbers
The rate per period is the annual rate ÷ periods per year, and payments occur once per period.
Results
$59,777.15
Present value
$120,000.00
Total of the payments
$60,222.85
Value lost to discounting
0.666667%
Rate per period
240
Number of periods
0.202971
Discount factor at the end
The working
PV = PMT × [1 − (1 + i)^−n] ÷ i = $500.00 × [1 − (1 + 0.00666667)^−240] ÷ 0.00666667 = $59,777.15
Discount factor table
| Period | Discount factor | Payment | Present value | Running total |
|---|---|---|---|---|
| 1 | 0.993377 | $500.00 | $496.69 | $496.69 |
| 2 | 0.986799 | $500.00 | $493.40 | $990.09 |
| 3 | 0.980264 | $500.00 | $490.13 | $1,480.22 |
| 4 | 0.973772 | $500.00 | $486.89 | $1,967.11 |
| 5 | 0.967323 | $500.00 | $483.66 | $2,450.77 |
| 6 | 0.960917 | $500.00 | $480.46 | $2,931.23 |
| 7 | 0.954553 | $500.00 | $477.28 | $3,408.50 |
| 8 | 0.948232 | $500.00 | $474.12 | $3,882.62 |
| 9 | 0.941952 | $500.00 | $470.98 | $4,353.59 |
| 10 | 0.935714 | $500.00 | $467.86 | $4,821.45 |
| 11 | 0.929517 | $500.00 | $464.76 | $5,286.21 |
| 12 | 0.923361 | $500.00 | $461.68 | $5,747.89 |
| 13 | 0.917246 | $500.00 | $458.62 | $6,206.51 |
| 14 | 0.911172 | $500.00 | $455.59 | $6,662.10 |
| 15 | 0.905138 | $500.00 | $452.57 | $7,114.67 |
| 16 | 0.899143 | $500.00 | $449.57 | $7,564.24 |
| 17 | 0.893189 | $500.00 | $446.59 | $8,010.84 |
| 18 | 0.887274 | $500.00 | $443.64 | $8,454.47 |
| 19 | 0.881398 | $500.00 | $440.70 | $8,895.17 |
| 20 | 0.875561 | $500.00 | $437.78 | $9,332.95 |
| 21 | 0.869762 | $500.00 | $434.88 | $9,767.83 |
| 22 | 0.864002 | $500.00 | $432.00 | $10,199.83 |
| 23 | 0.85828 | $500.00 | $429.14 | $10,628.97 |
| 24 | 0.852596 | $500.00 | $426.30 | $11,055.27 |
| 25 | 0.84695 | $500.00 | $423.48 | $11,478.75 |
| 26 | 0.841341 | $500.00 | $420.67 | $11,899.42 |
| 27 | 0.835769 | $500.00 | $417.88 | $12,317.30 |
| 28 | 0.830234 | $500.00 | $415.12 | $12,732.42 |
| 29 | 0.824736 | $500.00 | $412.37 | $13,144.79 |
| 30 | 0.819274 | $500.00 | $409.64 | $13,554.42 |
| 31 | 0.813849 | $500.00 | $406.92 | $13,961.35 |
| 32 | 0.808459 | $500.00 | $404.23 | $14,365.58 |
| 33 | 0.803105 | $500.00 | $401.55 | $14,767.13 |
| 34 | 0.797786 | $500.00 | $398.89 | $15,166.02 |
| 35 | 0.792503 | $500.00 | $396.25 | $15,562.28 |
| 36 | 0.787255 | $500.00 | $393.63 | $15,955.90 |
| 37 | 0.782041 | $500.00 | $391.02 | $16,346.92 |
| 38 | 0.776862 | $500.00 | $388.43 | $16,735.35 |
| 39 | 0.771717 | $500.00 | $385.86 | $17,121.21 |
| 40 | 0.766606 | $500.00 | $383.30 | $17,504.52 |
| 41 | 0.76153 | $500.00 | $380.76 | $17,885.28 |
| 42 | 0.756486 | $500.00 | $378.24 | $18,263.52 |
| 43 | 0.751477 | $500.00 | $375.74 | $18,639.26 |
| 44 | 0.7465 | $500.00 | $373.25 | $19,012.51 |
| 45 | 0.741556 | $500.00 | $370.78 | $19,383.29 |
| 46 | 0.736645 | $500.00 | $368.32 | $19,751.61 |
| 47 | 0.731767 | $500.00 | $365.88 | $20,117.50 |
| 48 | 0.726921 | $500.00 | $363.46 | $20,480.96 |
| 49 | 0.722107 | $500.00 | $361.05 | $20,842.01 |
| 50 | 0.717324 | $500.00 | $358.66 | $21,200.67 |
| 51 | 0.712574 | $500.00 | $356.29 | $21,556.96 |
| 52 | 0.707855 | $500.00 | $353.93 | $21,910.89 |
| 53 | 0.703167 | $500.00 | $351.58 | $22,262.47 |
| 54 | 0.69851 | $500.00 | $349.26 | $22,611.73 |
| 55 | 0.693884 | $500.00 | $346.94 | $22,958.67 |
| 56 | 0.689289 | $500.00 | $344.64 | $23,303.31 |
| 57 | 0.684724 | $500.00 | $342.36 | $23,645.67 |
| 58 | 0.68019 | $500.00 | $340.09 | $23,985.77 |
| 59 | 0.675685 | $500.00 | $337.84 | $24,323.61 |
| 60 | 0.67121 | $500.00 | $335.61 | $24,659.22 |
Showing the first 60 of 240 periods.
How to Use the Present Value Calculator
- 1. Choose the cash flow. A single future amount, a series of equal payments (an annuity), or a payment that continues forever (a perpetuity).
- 2. Enter the amount and the rate. The discount rate is a nominal annual rate. Pick how many periods a year it is applied: for an annuity this is also how often a payment is made.
- 3. Enter the time. In years — 20 years of monthly payments is 240 periods. A perpetuity needs no end date, but can grow by a fixed percentage each period.
- 4. Set the timing for payments. At the end of each period is an ordinary annuity; at the start is an annuity due, which is worth more because every payment arrives one period sooner.
- 5. Read the result and the table. The present value, the working and a table of discount factors appear below.
What Present Value Means
Money received later is worth less than the same money today, because today's money could be earning a return in the meantime. Present value converts a future amount into today's money by dividing it by the growth it would have earned: PV = FV ÷ (1 + i)n, with i the rate per period and n the number of periods. The factor 1 ÷ (1 + i)n is the discount factor, and the rate you use is the discount rate.
Choosing the discount rate is the judgement call. It might be the interest rate on a loan, the return you could earn elsewhere, or a required return set by the problem. The calculator treats it as given and does not suggest one.
The Three Formulas
| Cash flow | Present value |
|---|---|
| Single amount | PV = FV ÷ (1 + i)n (or FV × e−rt for continuous discounting) |
| Ordinary annuity | PV = PMT × [1 − (1 + i)−n] ÷ i |
| Annuity due | PV = PMT × [1 − (1 + i)−n] ÷ i × (1 + i) |
| Perpetuity | PV = PMT ÷ i |
| Growing perpetuity | PV = PMT ÷ (i − g), with i greater than g |
These match the conventions of Excel's PV function: type 0 is end-of-period, type 1 is beginning-of-period, and the rate is the rate per period. The calculator is tested against Excel's documented example, in which 500 received monthly for 20 years at 8% a year has a present value of 59,777.15.
Worked Examples
- Single amount. 10,000 due in 5 years at 8% a year, compounded annually, is worth 10,000 ÷ 1.085 = 6,805.83 today. Discounted monthly at 8% it is 6,712.10, and continuously (10,000 × e−0.4) it is 6,703.20.
- Annuity. 500 at the end of each month for 20 years at 8% (i = 0.08 ÷ 12, n = 240) has a present value of 59,777.15, although the payments add up to 120,000. The other 60,222.85 is the value lost to discounting. If each payment is made at the start of the month, the value rises by a factor of 1 + i to 60,175.66.
- Perpetuity. A payment of 1,000 a year forever at 5% is worth 1,000 ÷ 0.05 = 20,000. If the payment grows 2% a year and the rate is 7%, the value is 1,000 ÷ (0.07 − 0.02) = 20,000 as well.
Read the discount factor table
Each factor is the value today of 1 received at that time. The first rows are close to 1 and the factor falls as the date moves out, which is why distant payments add little to the total. For an annuity the running total column is the present value of the payments so far; its last row is the answer above.
Common Mistakes
- Mixing annual and periodic rates. A monthly annuity needs a monthly rate, the annual rate ÷ 12, and 12 periods a year. The calculator does this conversion from the annual rate you enter.
- Forgetting annuity due. Rent, insurance premiums and tuition are often paid at the start of the period. That changes the value by a full period of interest.
- Discounting a perpetuity at a rate at or below its growth. The sum does not converge; the calculator reports that instead of returning a number.
- Treating the answer as a price. Present value is a model. Fees, taxes, risk and the choice of discount rate all move a real price, and nothing here is financial advice.
Frequently Asked Questions
- What is the formula for present value?
- For a single amount, PV = FV ÷ (1 + i)n, where i is the rate per period and n the number of periods. For equal payments, PV = PMT × [1 − (1 + i)−n] ÷ i. For a perpetuity, PV = PMT ÷ i.
- What is the difference between an ordinary annuity and an annuity due?
- An ordinary annuity pays at the end of each period; an annuity due pays at the start. Every payment of an annuity due arrives one period earlier, so its present value is the ordinary value multiplied by (1 + i).
- What discount rate should I use?
- It depends on the question: the interest rate on the debt you would repay, the return available on an alternative use of the money, or the rate your course problem gives you. A higher rate lowers the present value. The calculator does not recommend a rate.
- How do I find the present value of a lump sum due in the future?
- Choose A single future amount, enter the amount, the annual discount rate, how often it is compounded and the years. Ten thousand due in five years at 8% compounded annually has a present value of 6,805.83.
- How is present value related to NPV?
- Net present value is the sum of the present values of all cash flows, with the initial outlay counted as negative. If you have uneven payments, enter each period's cash flow in the NPV and IRR Calculator.
- What is a perpetuity and does it have a finite value?
- A perpetuity is a payment that continues forever, such as a consol bond. It still has a finite present value, PMT ÷ i, because distant payments are discounted heavily. A growing perpetuity has a finite value only if the discount rate exceeds the growth rate.