Summary of Discrete Compounding Interest Factors
To Find
P
Given
F
F
P
P
Factor
Symbol
(P|F, i, n)
Description
Present Worth
(1 + i ) n
(F|P, i, n)
Compound Amount
A
(1 + i ) n − 1
i (1 + i ) n
(P|A, i, n)
Uniform Series, Present
Worth
A
P
i (1 + i ) n
(1 + i ) n − 1
(A|P, i, n)
Capital Recovery Factor
F
A
(F|A, i, n)
Uniform Series,
Compound Amount
A
F
(1 + i ) n − 1
i
i
(1 + i ) n − 1
(A|F, i, n)
Sinking Fund Factor
P
G
(P|G, i, n)
Gradient Series, Present
Worth
F
G
1 − (1 + ni )(1 + i ) − n
i2
n
⎛ 1 ⎞ ⎛ (1 + i ) − 1 ⎞
− n⎟
⎜ ⎟⎜
i
⎝ i ⎠⎝
⎠
(F|G, i, n)
Gradient Series,
Compound Amount
A
G
(A|G, i, n)
Arithmetic Gradient
Conversion
P
C
⎛1
⎞
n
⎜ −
⎟
n
⎝ i (1 + i ) − 1 ⎠
1 − (1 + k ) n (1 + i ) − n
i−k
(P|C, i, n)
Geometric Series, Present
Worth
(1 + i )
−n
Summary of Continuous Compounding Interest Factors
To Find
P
Given
F
F
P
P
A
A
P
F
A
A
F
P
G
A
G
Factor
− im n
e
eim n
eim n − 1
eim n (eim − 1)
eim n (eim − 1)
eim n − 1
eim n − 1
eim − 1
eim − 1
eim n − 1
eim n − 1 − n(eim − 1)
eim n (eim − 1) 2
1
n
− im n
im
e −1 e −1
Symbol
(P|F, im, n)∞
Description
Present Worth
(F|P, im, n) ∞
Compound Amount
(P|A, im, n) ∞
Uniform Series, Present
Worth
(A|P, im, n) ∞
Capital Recovery Factor
(F|A, im, n) ∞
Uniform Series,
Compound Amount
(A|F, im, n) ∞
Sinking Fund Factor
(P|G, im, n) ∞
Gradient Series, Present
Worth
(A|G, i, n) ∞
Arithmetic Gradient
Conversion
ie  (1  i ) m  1
ie  eim  1
minal interestt rate 
 1  Nom
Real innterest rate  
 1
I
ratee
1  Inflation


i 
ߩ௫௬ ൌ
௖௢௩
௩ೣ೤
ఙೣఙ೤
cov
v(ri , rm )
m
E i }  rf   i 
E{r
2
 r    2 r  
 p  r  Er 
i 1
E{rm }  rf 



equity or mark
ket risk premium
n
2
i
i