How do I calculate the present value?
Divide the future amount by one plus the rate, raised to the number of periods. For $100,000 in 10 years at 5%, that's $100,000 ÷ 1.05^10 = $61,391.33. Money later is worth less than money now, because money now can earn a return.
PV = FV ÷ (1 + r)^n| Years away | 3% | 4% | 5% | 6% | 7% | 8% |
|---|---|---|---|---|---|---|
| 1 | $970.87 | $961.54 | $952.38 | $943.40 | $934.58 | $925.93 |
| 5 | $862.61 | $821.93 | $783.53 | $747.26 | $712.99 | $680.58 |
| 10 | $744.09 | $675.56 | $613.91 | $558.39 | $508.35 | $463.19 |
| 20 | $553.68 | $456.39 | $376.89 | $311.80 | $258.42 | $214.55 |
| 30 | $411.99 | $308.32 | $231.38 | $174.11 | $131.37 | $99.38 |
The gap gets wide over long spans. $1,000 in 30 years is worth $412 at 3% and $99 at 8%. To account for rising prices, discount by inflation: at an example 3% rate, $100,000 in 20 years buys about what $55,368 buys today. The inflation calculator has more on this, with real price data.
How do you find future value with monthly contributions?
Grow the starting amount, then add the grown value of each payment. In this formula, i is the rate per period and n is the number of periods. For a lump sum, drop the payment part, which leaves the classic future value formula: the amount today times (1 + i)^n.
FV = PV × (1 + i)^n + PMT × ((1 + i)^n − 1) ÷ i| Monthly deposit | 10 years | 20 years | 30 years |
|---|---|---|---|
| $100 | $27,357 | $72,286 | $162,580 |
| $300 | $61,974 | $176,472 | $406,574 |
| $500 | $96,591 | $280,657 | $650,568 |
| $1,000 | $183,133 | $541,120 | $1,260,553 |
If you take money out instead, choose "Money I take out" and the payments subtract. This tool stops at $0 and tells you when the money runs out, while the raw formula shows a negative number. For deeper savings planning, with fees and different deposit schedules, use the compound interest calculator.
What is the present value of an annuity with monthly payments?
It's the amount that could fund those payments today. Payments of $500 a month for 20 years at 6% have a present value of $69,790. That's much less than the $120,000 you would receive in total. People use this to value pension payments, lease payments, or a structured settlement.
PV = PMT × (1 − (1 + i)^−n) ÷ i| Monthly payment | 10 years | 20 years | 30 years |
|---|---|---|---|
| $500 | $45,037 | $69,790 | $83,396 |
| $1,000 | $90,073 | $139,581 | $166,792 |
| $2,000 | $180,147 | $279,162 | $333,583 |
| $3,000 | $270,220 | $418,742 | $500,375 |
An ordinary annuity pays at the end of each period. An annuity due pays at the start, so each payment gets one more period and the value is multiplied by (1 + i). Paid at the start, the example above is worth $70,139, which is $349 more. Rent paid in advance is an annuity due. A loan with payments at the end of each month is ordinary.
For payments that rise each year, use the growing annuity option. $20,000 a year for 20 years at 5% has a present value of $249,244. Raise it 2% a year and the value is $293,308. Saving $3,000 a year for 25 years at 7% grows to $189,747, or $250,024 if you add 3% more each year. With monthly payments, this tool raises them once a year rather than monthly.
How does this match Excel PV, FV, RATE, and NPER?
This tool solves the same equation. It reproduces Microsoft's documented examples: =PV(8%/12, 240, 500) is about $59,777.15 in absolute terms, and =FV(12%/12, 12, -1000) is $12,682.50.
- Divide the rate and multiply the time by the same number. Monthly means rate/12 and years×12.
- Excel uses signs. Cash you pay out is negative, so =PV often shows a negative result, as in the example above.
- The last argument picks the timing: 0 is the end of each period, and 1 is the start.
- RATE returns a rate per period, so multiply it by 12 for a yearly number from monthly inputs.
To solve for the rate, enter the start, end, and time. $10,000 growing to $18,000 over 8 years is 7.62% a year. To solve for time, leave the time out. $500,000 paying out $3,000 a month at 4% lasts about 20.3 years, and $10,000 plus $300 a month at 6% reaches $100,000 in about 13.8 years.
What discount rate should I use, and when does this mislead?
No rate is correct for everyone. A common approach is what you could earn on money with similar risk. This matters a lot: $100,000 in 20 years is $55,368 at 3% and $21,455 at 8%. Try a range, and check the table of nearby rates that the tool shows.
Check how your rate compounds, too. 6% a year split monthly works out to 6.17% effective. If your rate is already effective, set "Rate is" to effective under advanced options. If your payments and compounding run on different schedules, such as monthly deposits with daily interest, use the savings calculator.
A present value assumes a payment is certain. A pension, a settlement, or an alimony stream can stop or change, and courts or plans may require set assumptions. For a legal or tax valuation, an actuary or attorney can apply the required rules. A personal estimate from this tool doesn't replace that. Workers compensation or lease valuations can have their own rules, so check those before relying on a number.
Common questions
What is the difference between present value and future value?
Present value tells you what a later amount is worth today. Future value tells you what an amount today grows to later. They use the same rate and the same formula, turned around.
Why does a higher discount rate lower present value?
A higher rate means today's money could grow faster, so you need less of it now to reach the same future amount.
How is present value different from NPV?
Present value gives the worth today of future cash. Net present value subtracts your upfront cost as well, and suits uneven project cash flows. Use the NPV calculator for that.
Can I include amounts that aren't equal?
Yes. Under advanced options, add one-time amounts by year, on top of or instead of the repeating payment. For present and future value, they move in the same direction as your payments.
What if the answer says no rate works?
That means the numbers can't connect, for example no starting amount and no payments. A negative rate is possible, and it means you end with less than you put in.
Sources
- PV function · Microsoft
- FV function · Microsoft
- NPER function · Microsoft
- RATE function · Microsoft