<Dl> <Dt> Annuity </Dt> <Dd> P V = A (1 − e − r t) e r − 1 (\ displaystyle \ PV \ =\ (A (1 - e ^ (- rt)) \ over e ^ (r) - 1)) </Dd> <Dt> Perpetuity </Dt> <Dd> P V = A e r − 1 (\ displaystyle \ PV \ =\ (A \ over e ^ (r) - 1)) </Dd> <Dt> Growing annuity </Dt> <Dd> P V = A e − g (1 − e − (r − g) t) (r − g) − 1 (\ displaystyle \ PV \ =\ (Ae ^ (- g) (1 - e ^ (- (r-g) t)) \ over ^ ((r-g)) - 1)) </Dd> <Dt> Growing perpetuity </Dt> <Dd> P V = A e − g e (r − g) − 1 (\ displaystyle \ PV \ =\ (Ae ^ (- g) \ over e ^ ((r-g)) - 1)) </Dd> <Dt> Annuity with continuous payments </Dt> <Dd> P V = 1 − e (− r t) r (\ displaystyle \ PV \ =\ (1 - e ^ ((- rt)) \ over r)) </Dd> </Dl> <Dd> P V = A (1 − e − r t) e r − 1 (\ displaystyle \ PV \ =\ (A (1 - e ^ (- rt)) \ over e ^ (r) - 1)) </Dd> <Dd> P V = A e r − 1 (\ displaystyle \ PV \ =\ (A \ over e ^ (r) - 1)) </Dd> <Dd> P V = A e − g (1 − e − (r − g) t) (r − g) − 1 (\ displaystyle \ PV \ =\ (Ae ^ (- g) (1 - e ^ (- (r-g) t)) \ over ^ ((r-g)) - 1)) </Dd>

Meaning and importance of time value of money