Time Value of Money
Definitions and Abbreviations
Abbreviation
Definition
annuity: a series of payments or receipts having three specific
characteristics:
a. each payment is the same amount
b. payments occur at the end of evenly spaced time
periods
c. there are a finite number of payments
annuity due: an annuity where the payments occur at the beginning of evenly
spaced time periods
CF0, CF1 , etc
cash flows: a series of payments or receipts or both. We do not assume the
same dollar amount for each, but we usually assume they are evenly spaced
in time. The subscript indicates the time period.
EAR
effective annual [interest] rate: the annual interest rate that reflects the
effects of compounding
FV
future value: the accumulated value of an investment once all payments are
made, including interest or return received
g
growth rate: we assume this is constant over time.
r or i or k
interest rate
lump sum: a single payment or receipt (in contrast with annuity or
perpetuity)
n or t
number of time periods: months, half-years, years, etc.
PMT or C
payment: the constant payment or receipt of an annuity or perpetuity
perpetuity: a series of payments that never ends, where each payment is the
same amount and the payments occur at the end of evenly spaced time
periods
PV
present value: the value today of an investment or loan, or the value before
any payments are made or return accumulated.
Time Value of Money Formulae
Future value of a lump sum:
FV = PV (1 + r ) n
Present value of a lump sum:
PV =
*Present value of a perpetuity:
FV
(1 + r ) n
PV =
PMT
r
Present Value of an annuity:
1

1
PVA = PMT  −

 r r( 1 + r ) n 
Future Value of an annuity:
 ( 1 + r )n − 1 
FVA = PMT 

r


Present Value of an annuity due:
1

1
PVA = PMT  −
( 1 + r )
 r r( 1 + r ) n 
Future Value of an annuity due:
 ( 1 + r )n − 1 
FVA = PMT 
( 1 + r )
r


*Present value of a perpetuity with constant growth:
PMT1 PMT0 (1 + g )
PV =
=
r−g
r−g
Present Value of an annuity with constant growth:
n
PMT1   1 + g  
PVA =
 
1 − 
r − g   1 + r  
Future Value of an annuity with constant growth:
 (1 + r ) n − (1 + g ) n 
FVA = PMT1 

(r − g )


m
Effective Annual Interest Rate:
APR 

EAR = 1 +
 −1
m 
