Time Value of Money formula
TIME VALUE OF MONEY FORMULA SHEET
#
TVM Formula For:
1
Future Value of a
Lump Sum. (FVIFi,n)
Compounded/Payments
(m) Times per Year
Annual Compounding
FVn = PV( 1 + i )n
2
FV
1 i
PV =
Present Value of a
Lump Sum. (PVIFi,n)
-n
Future Value of an
Annuity. (FVIFAi,n)
FVAn = CF
4
Present Value of an
Annuity. (PVIFAi,n)
1 - ( 1 + i )-n
PVAn = CF i 5
Present Value of
Perpetuity. (PVA )
6
Effective Annual Rate given the APR.
7
The length of time required for a PV to grow to a FV.
8
The APR required for a PV to grow to a FV.
9
Present Value of a Growing Annuity.
10
Present Value of a Growing
Perpetuity.
11
The length of time required for a series of PMT’s to grow to a future amount (FVAn).
12
EAR = APR
n=
(-m n)
m
-1
ln ( FV/PV) m ln (1 i/m)
FV
PV
i= m
EAR = ei - 1
n=
ln (FV/PV) i i=
ln (FV/PV) n [1/(m n)]
-1
n
(FVA)(i)
+1
CF ln (1 + i)
ln 1 n n=
(1/n)
1 g
1 i
(-i n)
CF0 1 g i g
PVA
ln
i
EAR = 1 m -1
PV = FV e
CF
[(1 i/m) m 1]
PVA
i
CF0 1 g
1
i g
PVAn
1 - 1 + i/m
PVAn = CF i/m ln (FV/PV) ln (1 + i )
FV i= PV
(-m n)
( 1 + i/m )(m n) - 1 i/m FVAn = CF
CF i FV
(i n) e or
PV = FV 1 i/m
( 1 + i )n - 1 i 3
n=
PV =
(m n)
(i n)
FVn = PV e
or
PV = FV( 1 + i )
The length of time required for a series of PMT’s to exhaust a specific present amount (PVAn).
FV
1 i/m
PV =
n
or
PVA
(m n)
FVn = PV 1 i/m
Continuous
Compounding
i m ln n= (PVA)(i)
CF
, ln (1 i)
m ln 1
n
for PVA(i) < CF
m
FVA m
+
CF i ln (1 i/m)
(PVA)(i/m)
CF
,
ln(1 i/m)
for PVA(i/m) < CF
Legend
i = APR, the nominal or Annual Percentage Rate m = the number of compounding periods per year ln = the natural logarithm, the logarithm to the base e
CF = PMT = the
#
TVM Formula For:
1
Future Value of a
Lump Sum. (FVIFi,n)
Compounded/Payments
(m) Times per Year
Annual Compounding
FVn = PV( 1 + i )n
2
FV
1 i
PV =
Present Value of a
Lump Sum. (PVIFi,n)
-n
Future Value of an
Annuity. (FVIFAi,n)
FVAn = CF
4
Present Value of an
Annuity. (PVIFAi,n)
1 - ( 1 + i )-n
PVAn = CF i 5
Present Value of
Perpetuity. (PVA )
6
Effective Annual Rate given the APR.
7
The length of time required for a PV to grow to a FV.
8
The APR required for a PV to grow to a FV.
9
Present Value of a Growing Annuity.
10
Present Value of a Growing
Perpetuity.
11
The length of time required for a series of PMT’s to grow to a future amount (FVAn).
12
EAR = APR
n=
(-m n)
m
-1
ln ( FV/PV) m ln (1 i/m)
FV
PV
i= m
EAR = ei - 1
n=
ln (FV/PV) i i=
ln (FV/PV) n [1/(m n)]
-1
n
(FVA)(i)
+1
CF ln (1 + i)
ln 1 n n=
(1/n)
1 g
1 i
(-i n)
CF0 1 g i g
PVA
ln
i
EAR = 1 m -1
PV = FV e
CF
[(1 i/m) m 1]
PVA
i
CF0 1 g
1
i g
PVAn
1 - 1 + i/m
PVAn = CF i/m ln (FV/PV) ln (1 + i )
FV i= PV
(-m n)
( 1 + i/m )(m n) - 1 i/m FVAn = CF
CF i FV
(i n) e or
PV = FV 1 i/m
( 1 + i )n - 1 i 3
n=
PV =
(m n)
(i n)
FVn = PV e
or
PV = FV( 1 + i )
The length of time required for a series of PMT’s to exhaust a specific present amount (PVAn).
FV
1 i/m
PV =
n
or
PVA
(m n)
FVn = PV 1 i/m
Continuous
Compounding
i m ln n= (PVA)(i)
CF
, ln (1 i)
m ln 1
n
for PVA(i) < CF
m
FVA m
+
CF i ln (1 i/m)
(PVA)(i/m)
CF
,
ln(1 i/m)
for PVA(i/m) < CF
Legend
i = APR, the nominal or Annual Percentage Rate m = the number of compounding periods per year ln = the natural logarithm, the logarithm to the base e
CF = PMT = the