Time Value of Money formula

TIME VALUE OF MONEY FORMULA SHEET
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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