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Excel’s TVM functions and the sign convention

◈ 8 cards

rate, nper, pmt, pv, fv, type — the argument list five functions share, and why PV comes out negative.

Five functions, one argument list

Every time-value problem has five variables: a rate per period, a number of periods (nper), a level payment per period (pmt), a present value (pv) and a future value (fv). Exactly one of them is unknown. Excel gives you one function per unknown — PV, FV, PMT, NPER, RATE — and each takes the other four as arguments, plus a sixth, type, which is 0 for end-of-period payments (the default) and 1 for beginning-of-period.

The order is always the same family:

Square brackets mean optional, defaulting to 0. Notice that RATE is the odd one out — since the rate is the unknown, nper moves to the front.

Worked example — a deposit and a target

Dana deposits $1,000 today at 5 % a year for three years. In Excel: =FV(0.05,3,0,-1000), which returns 1,157.63. Check it by hand: $1{,}000 \times 1.05^3 = 1{,}157.625$.

Why the minus sign on the 1,000? Because Excel treats every argument as a cash flow from your point of view. The deposit leaves your pocket, so it is negative; the future value comes back to you, so Excel returns it positive. Enter the deposit as +1000 instead and the function returns −1,157.63: the same magnitude, the opposite sign.

Now the other direction. Dana wants $2,000 in five years and can earn 4 %. =PV(0.04,5,0,2000) returns −1,643.85 — negative, because to receive 2,000 later you must pay out 1,643.85 now. Hand check: $2{,}000 / 1.04^5 = 1{,}643.854$.

Predicting the sign

The rule that predicts every sign: the function returns the cash flow that balances the ones you entered. Enter a positive pv into =PMT(rate,nper,pv) — you received a loan — and the payment comes out negative, because you repay it. Enter a negative pv and a positive fv into =NPER(…) and you get a sensible number of periods; enter both positive and Excel cannot find a period count at which money paid to you grows into more money paid to you, so it returns #NUM!. RATE fails the same way.

On the paper the marker generally wants the magnitude, and you can force a positive display with =-PV(…). But a stray minus inside a chain of cells propagates into every later answer, so decide the sign deliberately every time rather than fixing it at the end.

The two habits that survive the exam

  1. Write the argument list in your head before you type: rate, nper, pmt, pv or fv, type.
  2. Decide which flows are out of your pocket and enter them negative — the answer's sign will then read as money coming back to you.
FunctionSolves forArguments in orderPositive pventered →PVpresent valuerate, nper, pmt,[fv], [type]n/a — pv is theoutputFVfuture valuerate, nper, pmt,[pv], [type]negative FVPMTlevel paymentrate, nper, pv,[fv], [type]negative PMTNPERperiodsrate, pmt, pv,[fv], [type]#NUM! unless fvnegativeRATErate per periodnper, pmt, pv,[fv], [type],[guess]#NUM! unless fvnegativeEvery function returns the cash flow that balances the ones you entered.
The argument order is the one family in four arrangements; RATE moves nper to the front because rate is the thing being solved for.
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