Find what a future lump sum, or a stream of equal deposits, is worth today. Enter the number of compounding periods and the rate earned each period. You get the present value, the interest given up by waiting, and — for deposits — the matching future value and a period schedule.
Default plan at a glance
| Result | Future money ($1,000) | $100 deposits (end) |
|---|---|---|
| Present value | $558.39 | $736.01 |
| Future value | $1,000.00 | $1,318.08 |
| Total principal | — | $1,000.00 |
| Total interest | $441.61 | $318.08 |
Examples
$1,000 in 10 periods at 6%
A $1,000 amount due in 10 periods, discounted at 6% per period, is worth $558.39 today. Waiting those 10 periods would earn $441.61 of interest on that present value.
$100 a period for 10 periods, end of period
Ten $100 deposits at the end of each period, earning 6%, grow to $1,318.08. Discounted to today they are worth $736.01. Principal is $1,000 and interest is $318.08.
Same deposits at the beginning of each period
Move each $100 deposit to the start of the period and the same inputs finish at $1,397.16. The present value rises to $780.17 because every deposit earns interest in the period it is added.
Formula
A single future amount FV discounted at a per-period rate i (= I/Y ÷ 100) over N periods is
PV = FV / (1 + i)^N
Total interest on that tab is FV − PV — the growth you forgo by taking
cash today instead of waiting.
A level deposit PMT at the end of each period (ordinary annuity) is
PV = PMT × [ 1 − (1 + i)^(−N) ] / i
FV = PMT × [ (1 + i)^N − 1 ] / i
Deposits at the beginning of each period (annuity due) earn one extra
period of interest, so both PV and FV are multiplied by (1 + i). When the
rate is 0%, present value equals the deposits themselves.
Match the rate to the period count. A 6% nominal annual rate compounded
monthly uses 0.5% per month and N in months. A 6% effective annual
rate instead uses ((1.06)^(1/12) − 1) × 100 ≈ 0.486755% per month.
These are different rate conventions. For monthly deposits, also enter PMT
as the amount deposited each month.
Assumptions and limits
The discount rate is constant and every period has equal length. Present value is sensitive to the chosen rate; it does not establish market value or account for taxes, fees, credit risk, liquidity, or uneven cash flows. Test several rates when the appropriate discount rate is uncertain.