Introduction to Corporate Finance

3: The Time Value of Money

3.3a =×∑ +

−

=

FV CFt (1 r)nt

t

n

1

3.4 FV PMT

r

r

[(1)n 1]

=×

 +−











3.5 =×
 +−









FVannuity duePMT ×+

r

r

() r

[(1)1]

(1 )

n

3.6 =×∑
= +

PVCF

r

1

(1 )

t

t

n

t

1

3.7 =×−

• 
  











PV 

PMT

rr

1

1

(1 )n

3.8 =×−

• 
  











PVannuity due ×+

PMT

rr

() 1 r

1

(1 )

n (1 )

3.10 PVP=×MT =
r

PMT

r

1

3.11 =
−

PV >

CF

rg

(^1) rg
3.12 =×+




×
FV PV
r
m
1
mn
3.13 FV (continuous compounding) = PV × (e r × n)
3.14 (^) =+



EAR −
r
m
11
m
3.14a EAR (continuous compounding) = e r – 1
KEY TERMS
annual percentage yield
(APY), 99
annuity, 79
average annual percentage
rate (AAPR), 99
annuity due, 81
compound interest, 69
continuous compounding, 97
discounting, 73
effective annual rate (EAR), 98
future value, 67
Gordon growth model, 94
growing perpetuity, 94
loan amortisation, 100
loan amortisation schedule, 100
mixed stream, 79
ordinary annuity, 81
perpetuity, 92
present value, 68
principal, 68
quarterly compounding, 96
semiannual compounding, 96
simple interest, 68
stated annual rate, 98
time line, 70
time value of money, 67
SELF-TEST PROBLEMS
Answers to Self-test problems and the Concept review questions throughout the chapter appear on
CourseMate with SmartFinance Tools at http://login.cengagebrain.com.
ST3-1 Starratt Alexander is considering investing specified amounts in each of four investment
opportunities described below. For each opportunity, determine the amount of money Starratt will
have at the end of the given investment horizon.