
7.13 The Present Value with Compounding
PV 5
FV
ð11ðr=mÞÞ
nm
7.14 The Present Value of a Cash Flow Series
PV 5
X
n
j51
FV
j
ð11ðr=mÞÞ
j
7.15 The Present Value of an Annuity with Continuous
Compounding
PV
acp
5
1 2 e
2rt
r
7.16 The Present Value of a Growing Annuity with
Continuous Compounding
PV
ga
5
PMTð1 2 e
2rt1gt
Þ
e
r2g
2 1
7.17 The Net Present Value of a Cash Flow Series
NPV 5
X
n
j21
CF
j
ð11rÞ
j
7.18 Expanded Net Present Value Formula
NPV 5
X
T
T50
CF
T
ð11rÞ
T
128 Mathematical Formulas for Industrial and Mechanical Engineering