Lump sum future value is FV = PV(1 + r)ⁿ, present value PV = FV/(1 + r)ⁿ. Annuity future value FVA = P[(1 + r)ⁿ − 1]/r, present PVA = P[1 − (1 + r)⁻ⁿ]/r. Perpetuity PVP = P/r, growing PVGP = P/(r − g). Doubling time DP = 72/r. Luca Pacioli wrote the rule of 72 in 1494, and Martín de Azpilcueta shaped the time value idea in the 1500s.
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