Present Value Calculator

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Present Value Calculator

Find what a future amount or a stream of payments is worth today at a given interest rate, or turn it around and find what money today grows to. Lump sums, regular payments, any compounding, with the discount factor and a year by year schedule.

Every figuretap a card to copy its value

Value over time

Year by year

Present value = FV ÷ (1 + i) to the power n + PMT × (1 − (1 + i) to the power −n) ÷ i. Future value = PV × (1 + i) to the power n + PMT × ((1 + i) to the power n − 1) ÷ i. Here i is the annual rate divided by the periods a year and n is the number of periods; payments at the start of each period are multiplied by (1 + i). Continuous compounding uses e to the power of the rate × years. Amounts work in any currency. The CSV, image and printed report contain the values you entered, nothing preloaded.

How to use this tool

Choose whether you want the present value, what future money is worth today, or the future value, what money today grows to. Enter the lump sum, a regular payment, or both, then the interest rate, the number of years and how often interest compounds. The result comes with the discount factor, the effective annual rate, a chart of the balance over time and a year by year schedule that proves the answer.

The setting people most often get wrong is the frequency. Payments here happen as often as interest compounds, so $500 a month needs monthly compounding, and the rate you enter is always the yearly rate: the calculator divides it by the number of periods for you. Entering a monthly rate as the yearly rate gives an answer that is wildly off.

What the calculation is doing

Money today can earn interest, so a dollar now is worth more than a dollar later. Compounding runs time forward: at 5% a year, $1 grows to 1.05 after a year and 1.05 to the power 10, or 1.6289, after ten. Discounting runs it backward: $1 received in ten years is worth 1 ÷ 1.6289 = $0.6139 today. That 0.6139 is the discount factor, and multiplying any future amount by it gives its present value.

A stream of payments is valued by discounting each payment by its own number of periods and adding them up. For equal payments that sum has a closed form, payment × (1 − (1 + i) to the power −n) ÷ i. Later payments shrink more, so $1,000 a year for 20 years at 6% is worth $11,469.92 today, not $20,000.

Curves showing the present value of $10,000 received up to 30 years away at 3%, 5% and 8%, falling to $4,120, $2,314 and $994 at 30 years, with $6,139.13 marked at 10 years and 5%; beside it bars of $1,000 paid each year for 20 years against its present value at 6%, falling from $943.40 in year 1 to $311.80 in year 20 and adding up to $11,469.92
Discounting bites hardest far away: at 8% a payment 30 years out is worth less than a tenth of its face value today.

Choosing the rate, and what the answer really means

Present value answers one question: how much would you need to invest today, at this rate, to produce these future amounts? The schedule below the chart shows exactly that, starting from the present value and ending at the future amount. That makes the choice of rate the whole argument. Use the return you could realistically get elsewhere for the same risk, or the rate on debt you could pay down instead.

The rate also decides how much the far future counts. At 3% a sum 30 years away keeps 41% of its value; at 8% it keeps under 10%. That is why long projects, pensions and lawsuits over future earnings are argued so fiercely over the discount rate, and why a small change to it can swing a valuation by a large amount.

Payment timing matters too. Loans and most investments pay at the end of each period, an ordinary annuity. Rent, leases and insurance premiums are paid at the start, an annuity due, and because every payment arrives one period sooner it is worth (1 + i) times more. A bond combines both ideas: the coupons are an annuity and the face value is a lump sum at the end, so its price is the present value of the two added together.

Discount factors

The value today of $1 received this many years away, with annual compounding. Multiply any future amount by the factor to get its present value.

Years away3%5%7%10%
10.97090.95240.93460.9091
50.86260.78350.71300.6209
100.74410.61390.50830.3855
150.64190.48100.36240.2394
200.55370.37690.25840.1486
300.41200.23140.13140.0573

A worked example you can check on paper

$10,000 received in 10 years, at 5% a year compounded yearly. The growth factor is 1.05 to the power 10 = 1.628895, so the discount factor is 1 ÷ 1.628895 = 0.613913 and the present value is 10,000 × 0.613913 = $6,139.13. Check it forwards: 6,139.13 × 1.628895 = $10,000.00.

Now $1,000 at the end of each year for 20 years at 6%. 1.06 to the power −20 = 0.311805, so the annuity factor is (1 − 0.311805) ÷ 0.06 = 11.469921 and the present value is 1,000 × 11.469921 = $11,469.92. Paid at the start of each year instead, it is 11,469.92 × 1.06 = $12,158.12.

A bond paying $50 a year for 10 years and $1,000 at the end, valued at 6%: the coupons are worth 50 × 7.360087 = $368.00 and the face value 1,000 × 0.558395 = $558.39, together $926.40. The bond trades below $1,000 because its 5% coupon is less than the 6% the market wants.

Mistakes that catch people out

Using the yearly rate as the period rate. With monthly payments the rate per period is the yearly rate ÷ 12, and the number of periods is years × 12. The calculator does the division; do not do it twice.

Mixing real and nominal figures. If the future amounts are in today’s prices, use a rate after inflation. If they will rise with prices, use a rate that includes inflation. Mixing the two overstates or understates the answer.

Getting the timing wrong. Payments in advance are worth more than payments in arrears. Set the timing to match when the money actually moves.

Counting periods from the wrong date. A payment one year away is discounted once, not zero times. The first payment of an ordinary annuity is one full period from today.

Treating the answer as certain. Present value assumes the payments arrive as promised. A risky promise deserves a higher rate, which lowers its value today.

Popular calculations

Each opens the calculator with those values filled in, and they can be changed once it is open. Compounding is yearly unless stated, and payments follow the compounding frequency.

Present value of a future amount

$10,000 in 10 years at 5%: $6,139.13$1,000 in 5 years at 3%: $862.61$100,000 in 20 years at 4%: $45,638.69$50,000 in 15 years at 6%: $20,863.25$1,000,000 in 30 years at 7%: $131,367.12$10,000 in 10 years at 5%, monthly: $6,071.61$10,000 in 10 years at 5%, continuous: $6,065.31$25,000 in 5 years at 8%: $17,014.58$1,000 in 1 year at 10%: $909.09

Present value of regular payments

$1,000 a year for 20 years at 6%: $11,469.92$100 a month for 10 years at 5%: $9,428.14$1,000 a month for 25 years at 4%: $189,452.48$2,000 a year for 10 years at 8%: $13,420.16$500 a month for 30 years at 7%: $75,153.78$1,000 a year for 10 years at 5%, in advance: $8,107.82

Bond style: payments plus a lump sum

$1,000 bond, $50 a year, 10 years at 6%: $926.40$1,000 bond, $25 every six months, 10 years at 6%: $925.61$1,000 bond, $40 a year, 5 years at 5%: $956.71

Future value of money today

$5,000 today for 30 years at 7%: $38,061.28$10,000 today for 10 years at 5%: $16,288.95$1,000 today for 20 years at 8%: $4,660.96$100 today for 50 years at 10%: $11,739.09$10,000 today for 10 years at 5%, monthly: $16,470.09

Future value of regular savings

$500 a month for 30 years at 7%: $609,985.50$100 a month for 40 years at 8%: $349,100.78$200 a month for 10 years at 5%: $31,056.46$6,000 a year for 30 years at 7%: $566,764.72$1,000 a month for 20 years at 6%: $462,040.90

How this was checked

The formulas are the standard time value of money factors, and the results were checked against textbook values: $10,000 in 10 years at 5% is worth $6,139.13, $1,000 a year for 20 years at 6% is worth $11,469.92, $5,000 grows to $38,061.28 over 30 years at 7%, and $500 a month for 30 years at 7% grows to $609,985.50. Every schedule was checked to start at the present value and end at the future amount to the cent, with payments added or taken off each period, and the annuity due results were checked by running the schedule with payments at the start of each period.

Every address in the lists above was then opened and checked for a distinct title, the right value, a chart that renders, and clean CSV, image and print output containing only the values entered, at desktop, tablet and phone widths.

Common questions

What is present value?

The amount of money today that is worth the same as a sum received later, given an interest rate. $10,000 in 10 years is worth $6,139.13 today at 5%, because $6,139.13 invested at 5% a year grows to exactly $10,000 in 10 years.

How do you calculate present value?

Divide the future amount by (1 + rate) raised to the number of periods. For a stream of equal payments, multiply the payment by (1 − (1 + rate) to the power −periods) ÷ rate. With monthly compounding, use the annual rate divided by 12 and the number of months.

What discount rate should I use?

The return you could earn elsewhere on money with similar risk, or the interest rate you pay if the money would otherwise reduce a debt. A safe government bond yield suits guaranteed payments; a business project needs a higher rate to reflect its risk. Try a couple of rates to see how much the answer depends on it.

What is the difference between present value and future value?

They are the same calculation run in opposite directions. Future value compounds money forward: $6,139.13 at 5% for 10 years becomes $10,000. Present value discounts it back: $10,000 in 10 years is $6,139.13 today.

What is an annuity due?

A payment stream where each payment comes at the start of the period, like rent or a lease, rather than at the end, like most loan payments. Each payment arrives one period sooner, so the value is (1 + rate) times higher: $1,000 a year for 10 years at 5% is worth $7,721.73 paid at the end of each year but $8,107.82 paid in advance.

How is present value related to net present value?

Net present value is the present value of all the money coming in minus the present value of the money going out, including any cost today. A project that costs $9,000 now and pays $10,000 in 2 years has a net present value of 10,000 ÷ 1.05 squared − 9,000 = $70.29 at 5%, so it just beats investing at 5%.

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