PV
Calculate what a series of equal future payments is worth today — how much you can borrow for a given payment, or what an annuity costs.
Syntax
PV(rate, nper, pmt, [fv], [type])| Argument | Required | Description |
|---|---|---|
rate | Required | The interest rate per period. |
nper | Required | The number of payments. |
pmt | Required | The payment each period. Money paid out is negative. |
fv | Optional | A lump sum at the end, in addition to the payments. Defaults to 0. |
type | Optional | 0 (the default) for payments at the end of each period, 1 for the start. |
Examples
Every example below was executed against VisiGrid engine 0.54.0 — not
transcribed from another vendor's documentation. Reproduce any of them with vgrid calc.
| Formula | Result | Notes |
|---|---|---|
=PV(0.05/12,360,-1073.64) | 199999.40 | The mortgage a 1,073.64 monthly payment supports — PMT run backwards. The 0.60 is the rounding in the typed payment. |
=PV(0.08,20,-1000) | 9818.15 | 1,000 a year for twenty years, discounted at 8%. |
=PV(0.08,20,-1000,0,1) | 10603.60 | Paid at the start of each year instead, each payment is discounted one year less. |
=PV(0,10,-100) | 1000 | With no interest there is nothing to discount. |
How much can I borrow?
Turn the question around: given the payment you can afford, what loan does it
support? Enter the payment as a negative number — it is money going out — and
PV returns the amount borrowed:
=PV(0.05/12,360,-1500)That is the largest 30-year loan at 5% a 1,500 monthly payment will clear.
Equal payments only
PV assumes the same payment every period. When the amounts differ — a project
with uneven returns, a lease with steps — use NPV, which
takes each cash flow separately.
Pricing an annuity
An annuity paying 1,000 a year for twenty years is worth 20,000 in total but
only about 9,818 today at 8%, because money received later is worth less. That
gap is the whole point of discounting, and PV is the direct way to measure it.
Excel compatibility
Matches Excel, including the sign convention and the optional fv and type arguments.