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Present Value

PV=FV(1+r)t\mathit{PV} = \frac{\mathit{FV}}{(1 + r)^{t}}

Worked example: $10,000 in 8 yr at 5% → PV = 6768.39 — press Try an example to run it live, then adjust anything.

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Present Value explained

PVFVrt

Money later is worth less than money now, because money now could be invested. Present value runs compound growth in reverse: $10,000 arriving in 8 years, discounted at 5% per year, is worth PV = 10000 / 1.05⁸ ≈ $6,768.39 today. Enter the rate as a decimal (5% → 0.05).

This one discount is the atom of finance — bond prices, mortgage balances, and a company's valuation are all sums of future cash flows each pulled back to today. Solving for r asks "what return does this deal imply?", and solving for t asks how long a target takes at a given rate.

Present Value formula

PV=FV(1+r)t\mathit{PV} = \frac{\mathit{FV}}{(1 + r)^{t}}
Where
  • PV\mathit{PV}= Present value
  • FV\mathit{FV}= Future value
  • rr= Discount rate per period (decimal)
  • tt= Number of periods

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Part of this formula set

Time value of money

4 formulasSimple interest, periodic and continuous compounding, and discounting a future amount back to what it is worth today.