Principles of Managerial Finance

192 PART 2 Important Financial Concepts

TABLE 4.9 Summary of Key Definitions, Formulas, and

Equations for Time Value of Money

Definitions of variables

eexponential function2.7183

EAReffective annual rate

FVnfuture value or amount at the end of period n

FVAnfuture value of an n-year annuity

iannual rate of interest

mnumber of times per year interest is compounded

nnumber of periods—typically years—over which money earns a return

PMTamount deposited or received annually at the end of each year

PVinitial principal or present value

PVAnpresent value of an n-year annuity

tperiod number index

Interest factor formulas

Future value of a single amount with annual compounding:

FVIFi,n(1i)n [Eq. 4.5; factors in Table A–1]

Present value of a single amount:

PVIFi,n [Eq. 4.11; factors in Table A–2]

Future value of an ordinary annuity:

FVIFAi,n

n

t=1

(1i)t^1 [Eq. 4.13; factors in Table A–3]

Present value of an ordinary annuity:

PVIFAi,n

n

t=1

[Eq. 4.15; factors in Table A–4]

Future value of an annuity due:

FVIFAi,n(annuity due)FVIFAi,n(1i) [Eq. 4.17]

Present value of an annuity due:

PVIFAi,n(annuity due)PVIFAi,n(1i) [Eq. 4.18]

Present value of a perpetuity:

PVIFAi,∞ [Eq. 4.19]

Future value with compounding more frequently than annually:

FVIFi,n 1  

mn

[Eq. 4.20]

for continuous compounding, m∞:

FVIFi,n (continuous compounding)ein [Eq. 4.22]

to find the effective annual rate:

EAR 1  

m

 1 [Eq. 4.23]

Basic equations

Future value (single amount): FVnPV(FVIFi,n) [Eq. 4.6]

Present value (single amount): PVFVn(PVIFi,n) [Eq. 4.12]

Future value (annuity): FVAnPMT(FVIFAi,n) [Eq. 4.14]

Present value (annuity): PVAnPMT(PVIFAi,n) [Eq. 4.16]

i

m

i

m

^1

i

^1

(1i)t

^1

(1i)n