Present Value Calculator
Find what a future sum is worth today, or what money today grows to, with any compounding, regular payments and inflation.
A growing annuity.
Shows the future amount in today's money.
Year-by-year discount table and chart
| Year | Discount factor | Future amount if paid then, worth today | Balance | Paid | Paid, worth today |
|---|
How your present value is worked out
Money later is worth less than money now, because money now can earn interest. So we shrink the future amount back to today.
- 1
Rate per period
6% ÷ 1= 6% a year
- 2
Growth factor
1.06^5= 1.338226
- 3
Shrink it to today
$10,000 ÷ 1.338226= $7,472.58
- 4
What waiting costs
$10,000 − $7,472.58= $2,527.42
Read more: the formula, a worked example and present vs future value
Present value (PV) is what money you will get later is worth now. It works the other way round from compound interest: instead of growing today's money forward, you shrink a future amount back, using a discount rate, the return you could earn on the money in the meantime (or the rate a lender, investor or court uses). Future value (FV) is the same sum done forwards. This calculator handles both, solves for the rate or the years too, and can add a stream of regular payments. It is plain time-value-of-money maths with no tax or fees. For a list of uneven cash flows see the NPV & IRR calculator, and for payments on their own the annuity calculator.
The formula
present value = future amount ÷ (1 + yearly rate ÷ m)^(m × years)
compounded continuously: present value = future amount × e^(−yearly rate × years)
future value = present value × (1 + yearly rate ÷ m)^(m × years)
rate = m × ((future ÷ present)^(1 ÷ (m × years)) − 1)
years = ln(future ÷ present) ÷ (m × ln(1 + yearly rate ÷ m))
Here m is how many times a year interest is added (1 yearly, 12 monthly, 365 daily). With regular payments P, n of them, at a rate per payment i = (1 + yearly rate ÷ m)^(m ÷ payments a year) − 1:
payments worth today = P × (1 − (1 + i)^−n) ÷ i
annuity due (paid at the start): × (1 + i)
present value = future amount worth today + payments worth today
(money you add instead: future amount worth today − payments worth today)
growing perpetuity = P ÷ (rate − growth)
today's money = future amount ÷ (1 + inflation)^years
Worked example
10,000 that you will get in 5 years, at a 6% yearly discount rate, compounded yearly:
- Growth factor: 1.065 = 1.06 × 1.06 × 1.06 × 1.06 × 1.06 = 1.338226 (1.3382255776).
- Present value = 10,000 ÷ 1.3382255776 = 7,472.58. The discount factor is 1 ÷ 1.3382255776 = 0.747258.
- Waiting 5 years costs 10,000 − 7,472.58 = 2,527.42: the interest 7,472.58 would earn at 6% in that time.
- Check it forwards: 7,472.58 × 1.3382255776 = 9,999.998, which is 10,000.00 to the cent (the present value was rounded to the cent).
- Compounded monthly instead: (1 + 0.06 ÷ 12)60 = 1.00560 = 1.348850, so PV = 10,000 ÷ 1.348850 = 7,413.72. Continuously: e0.3 = 1.349859, so PV = 7,408.18.
- Add 200 at the end of every month for those 5 years (monthly compounding): i = 0.005, n = 60, (1 − 1.005−60) ÷ 0.005 = (1 − 0.741372) ÷ 0.005 = 51.7256, so the payments are worth 200 × 51.7256 = 10,345.11 and the total is 10,345.11 + 7,413.72 = 17,758.83 today.
- With 3% inflation, 10,000 in 5 years buys what 10,000 ÷ 1.035 = 10,000 ÷ 1.159274 = 8,626.09 buys today.
Present value of 1 (discount factors)
What 1 paid in a number of years is worth today, compounded yearly. Multiply by your amount.
| Years | 3% | 5% | 6% | 8% | 10% |
|---|---|---|---|---|---|
| 1 | 0.9709 | 0.9524 | 0.9434 | 0.9259 | 0.9091 |
| 5 | 0.8626 | 0.7835 | 0.7473 | 0.6806 | 0.6209 |
| 10 | 0.7441 | 0.6139 | 0.5584 | 0.4632 | 0.3855 |
| 20 | 0.5537 | 0.3769 | 0.3118 | 0.2145 | 0.1486 |
| 30 | 0.4120 | 0.2314 | 0.1741 | 0.0994 | 0.0573 |
Which discount rate to use
Use the return you could get elsewhere at a similar risk: a savings or deposit rate for a safe, promised payment; a bond yield for a fixed income; a higher expected return for a business or shares. A higher rate makes the future amount worth less today. To compare in today's buying power, use a rate above inflation or fill in the inflation box.
This is an illustration, not financial advice. Real offers (pension buyouts, structured settlements, lottery lump sums) also depend on fees, tax and risk, which are not included.
Common questions
What is present value?
It is what a sum of money in the future is worth today, because money you have now can earn interest. 10,000 that you will get in 5 years, at 6% a year, is worth 10,000 ÷ 1.06⁵ = 7,472.58 today. Put 7,472.58 away at 6% and it grows to 10,000 in 5 years.
How does compounding change the present value?
The more often interest is added, the faster money grows, so a future sum is worth a little less today. 10,000 in 5 years at 6% is worth 7,472.58 with yearly compounding, 7,413.72 with monthly and 7,408.18 with continuous compounding (10,000 × e^(−0.06 × 5)).
How do I find the present value of payments plus a lump sum?
Add the value today of each part. 200 at the end of every month for 5 years plus 10,000 at the end, at 6% a year compounded monthly, is worth 200 × 51.7256 + 7,413.72 = 17,758.83 today. If each payment comes at the start of the month (annuity due) it is worth 17,810.56.
How do I work out future value?
Multiply today's amount by (1 + rate per period) raised to the number of periods. 5,000 at 8% a year for 10 years grows to 5,000 × 1.08¹⁰ = 10,794.62. With 1,000 to start and 100 added every month for 10 years at 6% compounded monthly, you end with 18,207.33.
How do I find the rate or the number of years?
Rate = (future ÷ today)^(1 ÷ years) − 1 with yearly compounding: 5,000 growing to 8,000 in 6 years is 8.15% a year. Years = ln(future ÷ today) ÷ ln(1 + rate): money doubles at 7% in 10.24 years. With regular payments there is no simple formula, so the calculator tries rates or lengths until the numbers fit.
What are a growing annuity and a perpetuity?
A growing annuity's payments rise each year. 1,000 a year for 10 years, rising 3% a year, at 7% is worth 7,920.53 today. A perpetuity pays for ever and is worth payment ÷ (rate − growth): 1,000 a year rising 2% at 7% is worth 1,000 ÷ 0.05 = 20,000.
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