★ MONEY · GROWTH & INVESTING · PRESENT VALUE
$10,000 in 5 years at 10% is worth $6,209.21 today — the discount is $3,790.79. Work out the present value of any future sum, annuity or series: the discount factor, the formula, and the round trip back to the future value, all shown. This one is the PRESENT-VALUE tool — what a future sum is worth today — the future-value-calculator page is the FUTURE-VALUE tool — what a sum today grows to — not what it is worth now; the net-present-value-calculator page is the NPV tool — an investment minus its cost — not a single future sum; and the future-value-of-annuity-calculator page is the FUTURE-VALUE-OF-ANNUITY tool — what yearly payments grow to — not what they are worth today.
A $10,000 payment in 5 years at a 10% discount rate is worth $6,209.21 today — the discount factor is 0.620921323 and the discount is $3,790.79. Put your own future value, years and rate in: the annuity and perpetuity figures follow from the same rate.
It means that $10,000 arriving in 5 years is worth $6,209.21 today if money earns 10% a year. Put the $6,209.21 in an account at 10% and it grows to exactly $10,000 in five years: $6,209.21 × 1.10 is $6,830.13 after one year, $7,513.15 after two, $8,264.46 after three, $9,090.91 after four and $10,000.00 after five. The two amounts are the same deal seen from opposite ends — $10,000 in five years and $6,209.21 today are equivalent at a 10% return, and the $3,790.79 gap between them is what waiting costs. The discount factor is 0.620921: every future dollar is worth about 62 cents today, because five years of 10% growth turns 62 cents into a dollar.
The discount rate is the whole answer. At 5% the same $10,000 is worth $7,835.26, and at 15% it is worth $4,971.77 — the rate moves the answer by thousands, so a rate you guessed is a guess, not a valuation. Use the return you could actually earn on money of similar risk: a savings rate for a safe promise, a higher rate for a risky one. If the promise might not arrive at all, that risk belongs in the rate, not in wishful thinking.
Time shrinks value faster than it looks. Three years out the value is $7,513.15, five years out it is $6,209.21, ten years out it is $3,855.43 — doubling the wait from 5 to 10 years cuts the value by more than a third, because the discount compounds. A payment 20 years away at 10% keeps only about 15 cents on the dollar. Long-dated promises trade at steep discounts for this reason, not because anyone is being unfair.
A series is worth more than its last payment. A single $10,000 in five years is worth $6,209.21, but $2,000 a year for five years is worth $7,581.57 — more, because the early payments are discounted less. Discount each payment separately and add them up; the annuity factor 3.790786769 does that adding for you. And a payment that never stops is worth the payment divided by the rate: $2,000 a year forever at 10% is worth $20,000.00.
On the defaults: $10,000 in 5 years at a 10% discount rate.
And the other way: a present value of $5,000 at 10% over 5 years implies a future value of $8,052.55; a $10,000 payment worth $6,209.21 today over 5 years implies a discount rate of 10.00%; and the same figures imply 5.00 years.
The defaults are a single $10,000 payment in 5 years, discounted at 10% a year with annual compounding — the payment arrives at the end of year 5, the rate stays flat, and there is no tax, no inflation adjustment and no risk of non-payment in the number. Annual compounding is the convention here: if your payments compound monthly, use the monthly rate and count months instead, and the factor changes. The annuity figures assume the $2,000 arrives at the end of each year; payments at the start of each year are worth one more year of growth each. The perpetuity assumes the $1,000 a year never stops and never grows. Change the rate to the return you could actually earn before you trust the answer.
These notes repeat in every explainer section because this page is built to be read start to finish: the discount rate is the whole answer; time shrinks value faster than it looks; and a series is worth more than its last payment.
| Output | Formula | What it means |
|---|---|---|
| Present value | FV ÷ (1 + r)^n | $6,209.21 — what $10,000 in 5 years is worth today at 10%. |
| Discount factor | (1 + r)^−n | 0.620921 — each future dollar is worth 0.620921 today. |
| Discount factor (9dp) | (1 + r)^−n, unrounded | 0.620921323 — the unrounded factor, for checking spreadsheet work. |
| Discount — what waiting costs | FV − PV | $3,790.79 — the $10,000 minus the $6,209.21. |
| Annuity PV ($2,000/yr) | PMT × (1 − (1+r)^−n) ÷ r | $7,581.57 — $2,000 a year for 5 years at 10%. |
| Annuity factor (9dp) | (1 − (1+r)^−n) ÷ r, unrounded | 3.790786769 — the unrounded annuity factor. |
| Perpetuity ($2,000/yr) | PMT ÷ r | $20,000.00 — $2,000 a year forever at 10%. |
| Reverse: Find the future value | step | $8,052.55: PV $5,000.00 — $8,052.55 in 5 years at 10.00% (factor 0.620921). |
| Reverse: Find the discount rate | step | 10.00%: PV $6,209.21 — $10,000 in 5 years at 10.00% (factor 0.620921). |
| Reverse: Find the number of years | step | 5.00 years: PV $6,209.21 — $10,000 in 5 years at 10.00% (factor 0.620921). |
| 3 years instead of 5 | same model | PV $7,513.15 — $10,000 in 3 years at 10.00% (factor 0.751315). |
| 10 years instead of 5 | same model | PV $3,855.43 — $10,000 in 10 years at 10.00% (factor 0.385543). |
| 5% discount rate instead of 10% | same model | PV $7,835.26 — $10,000 in 5 years at 5.00% (factor 0.783526). |
| 15% discount rate instead of 10% | same model | PV $4,971.77 — $10,000 in 5 years at 15.00% (factor 0.497177). |
| $2,000 a year for 5 years (annuity) | same model | Annuity PV $7,581.57 — $2,000 a year for 5 years at 10.00% (annuity factor 3.790787). |
| $20,000 future value instead of $10,000 | same model | PV $12,418.43 — $20,000 in 5 years at 10.00% (factor 0.620921). |
| 0% discount rate | same model | PV $10,000.00 — $10,000 in 5 years at 0.00% (factor 1.000000). |
| 0 years | same model | PV $10,000.00 — $10,000 in 0 years at 10.00% (factor 1.000000). |
| -5% discount rate | same model | PV $12,923.55 — $10,000 in 5 years at −5.00% (factor 1.292355). |
| $0 future value | same model | PV $0.00 — $0 in 5 years at 10.00% (factor 0.620921). |
Figures are the model's own totals on the numbers you type, computed from unrounded values: the discount factor is (1 + r)^−n, the present value is the future value times the factor, and the annuity factor is (1 − (1+r)^−n) ÷ r — the displayed factor is rounded to 6dp (0.620921) and to 9dp (0.620921323) for checking, and the 9dp display uses the 1e-12 epsilon because the usual +1e-9 epsilon is itself the last digit at 9dp. The model assumes annual compounding, a flat discount rate, a payment at the end of the period, no tax, no inflation and no default risk. It does not know what return you can actually earn, and it cannot price risk: a promised $10,000 that might not arrive is worth less than the formula says. This page is a calculation tool, not financial advice: talk to a licensed adviser before you act on a valuation.
$10,000 in 5 years at a 10% discount rate is worth $6,209.21 today — discount factor 0.620921 (0.620921323 unrounded), discount $3,790.79. $2,000 a year for 5 years is worth $7,581.57 (annuity factor 3.790786769 unrounded); $2,000 a year forever is worth $20,000.00. At 3 years the value is $7,513.15; at 10 years it is $3,855.43; at 5% it is $7,835.26; at 15% it is $4,971.77. Source: Bright Side Kit, brightoolbox.com.
Present value is what a future sum is worth today: $10,000 in 5 years at 10% is worth $6,209.21. Money today can be invested and grow, so a future payment is worth less than its face value — the present value says exactly how much less.
Divide the future value by (1 + r)^n: $10,000 ÷ 1.10^5 = $6,209.21. The discount factor is 0.620921323, so every future dollar is worth about 62 cents today.
The return you could earn on money of similar risk — 10% on the defaults. The rate is the whole answer: at 5% the value is $7,835.26, at 15% it is $4,971.77.
$7,581.57 at 10%. Discount each payment separately and add them up — the annuity factor 3.790786769 does the adding: $2,000 × 3.790786769.
$20,000.00 at 10% — the payment divided by the rate. A perpetuity never stops, so its value is $2,000 ÷ 0.10.
Because the discount compounds: at 10% the 5-year value is $6,209.21 and the 10-year value is $3,855.43. Doubling the wait cuts the value by more than a third.
Then the present value equals the future value: $10,000 in 5 years is worth $10,000.00. With no return available, waiting costs nothing.
Yes, with a negative discount rate: at −5% the $10,000 is worth $12,923.55. A negative rate means money loses value in reverse — rare, but the math handles it.