FV / PV
FV projects what a series of regular contributions grows into by a future date; PV works backward, finding what a future amount (or payment stream) is worth today.
FV and PV are mirror images of the same compounding math, just pointed in opposite directions. FV answers "where does this end up": given a regular contribution and a rate, what balance results after a set number of periods. PV answers "what is that worth right now": given a future payment stream, what lump sum today would be equivalent to it at the same rate. A common PV use is valuing a series of future withdrawals, like a pension, in today's money, which is exactly what discounting is for.
Syntax
| Argument | Description |
|---|---|
| rate | Required for both. The interest rate per period, matching nper's units. |
| nper | Required for both. The number of periods. |
| pmt | Required for both. The regular payment or contribution each period: 0 if there isn't one. |
| pv | FV: Optional. Any lump sum already in the account at the start. PV: this is what PV itself solves for. |
| fv | PV: Optional. A target lump sum at the end, if there is one, separate from the payment stream. |
| type | Optional for both. 0 (end of period) or 1 (start of period). |
A real example: what a monthly savings plan grows into
$200 deposited monthly for 3 years at 5% annual interest:
The deposit is entered as a negative number, money leaving the saver's pocket each month, while the resulting balance FV returns comes back positive, following Excel's convention that money going out and money accumulating have opposite signs.
Worked examples
| A | B | C | |
|---|---|---|---|
| 1 | Monthly deposit | Annual rate | Months |
| 2 | -200 | 0.05 | 36 |
| A | B | C | |
|---|---|---|---|
| 1 | Monthly withdrawal | Annual rate | Months |
| 2 | -1500 | 0.04 | 240 |
Common mistakes
- Using an annual rate with a monthly nper, the same rate/period mismatch that trips up PMT. Divide the rate down to match whatever period nper counts in.
- Forgetting that a payment going out (a contribution or withdrawal) and an amount coming in (the resulting balance) are opposite signs in Excel's convention: mixing them up flips the result's sign.
- Reaching for FV when the question is really "what's this worth today" (that's PV), or vice versa. They solve for opposite ends of the same timeline.
Related functions
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