# Time Value of Money formula

Topics: Time value of money, Annual percentage rate, Compound interest Pages: 9 (385 words) Published: October 31, 2013
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 periodic payment or cash flow

n = the number of periods
EAR = the Effective Annual Rate
e = the base of the natural logarithm 2.71828…
(Calculator: 1
ex )
Perpetuity = an infinite annuity

Prepared by Jim Keys