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FV & PV

Finance

The two ends of time value: what a stream is worth today, and what a balance grows into.

Difficulty

Amateur

Excel file

1What is it?

PV discounts a future stream back to today — what you should pay now for money you'll receive later. FV does the opposite, growing a balance and a series of deposits forward. Between them they answer most of the questions that sound like finance: whether a payment plan beats paying cash, what a reserve will be worth in five years, whether a valuation someone handed you is remotely sane. Both use the same sign convention as the rest of the family, and both take a rate PER PERIOD.

2What it looks like

PV(rate, nper, pmt, [fv], [type])   ·   FV(rate, nper, pmt, [pv], [type])

rate: The rate per period — annual over 12 for monthly.
nper: Number of periods, counted in the same unit as the rate.
pmt: The payment made each period. Money leaving is negative. Use 0 when there's only a single lump sum.
[fv] / [pv]: The lump sum at the other end — a balloon payment, or an opening balance. 0 by default.
[type]: 0 (default) for end-of-period, 1 for beginning. An annuity due is type 1.

3When you use it

Decide whether a vendor's payment plan is cheaper than paying up front.
Value a fixed stream — a lease, a note, a support contract.
Project what a reserve or sinking fund reaches by a given date.

4See it in action

Change the inputs — the formula and result update live. Prefer the real thing? Download the Excel file and open it in Excel.

A fixed payment for a fixed term, discounted back. Raise the rate and today's value falls.

=PV(B2/100/12, B3, -B4)Worth today (PV): $15,956

	A	B	C
1	Input	Value	Result
2	Annual rate %		Worth today (PV): $15,956
3	Months		Worth at the end (FV): $20,268
4	Payment / month		Paid in cash over 36 months: $18,000

The lime cell holds the formula — click it (or any cell) to see its contents in the bar above, just like Excel. Edit the blue cells to watch it recompute.

Paid at

5Common errors

Result is negative and you expected positiveThis is the sign convention working, not a bug — Excel returns the flow in the opposite direction to the one you entered.

Fix: Enter payments as negative (money out) and read the answer as money in, or wrap the result in ABS for display only.

Answer is wildly too largeAn annual rate was used with a monthly nper.

Fix: Divide the rate and count the periods in the same unit — 8%/12 with 36 months.

The lump sum got ignoredpmt was left blank rather than 0 while passing fv or pv positionally.

Fix: Type the 0. Excel's positional arguments will otherwise read your lump sum as the payment.

Off by one periodAn annuity due (payments at the start) was left at the default type 0.

Fix: Pass type = 1 for rent, leases and anything paid in advance.

6Better functions & alternatives

NPV — Use NPV when the cash flows differ period to period; PV is for a level payment.
XNPV — Use when the flows are dated rather than evenly spaced.
PMT — The same equation solved for the payment instead.

Want FV & PV already wired into a model? Wauvel's free tools download as branded, formula-driven Excel.

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