# CHAPTER 2 time value of money.docx

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Professor FIN502 Personal Financial Planning
CHAPTER 2 time value of money
Time value of money: comparing monetary amounts that you pay or receive at different times
o Underlying concept of time value of money is rate of return
RATE OF RETURN SINGLE PERIOD
Discount bond: investment that pays no interest during its life
Discount rate: rate of interest or rate of return that we use to equate amounts of money paid or received
in different periods
o “CF0 is the value of CF1 discounted at k”
K = CF1 CF0 / CF0
K = rate of return
CF = cash flow
RATE OF RETURN MULTIPERIOD
Arithmetic mean return: take the sum and find the mean
Arithmetic mean average = ∑ (kt / n)
K = sum of rate of returns for t number of times
N = number of years
Geometric mean return: rate of return that would compound to the same final answer as individual rates
multiplied together
o Should be lower or equal to arithmetic mean return; difference would be large
Geometric mean average = [ (1 + kt)]1/n 1
(1 + kt) = multiply all the factors for the years
(1/n) = take the nth root
COMPOUNDING MORE FREQUENTLY THAN ANNUALLY
Annual percentage rate (APR): conventional method of quoting interest rates that ignores the
compounding effect
o Method is used for quoting rates for customer loans, residential mortgages,
corporate/commercial mortgages, other loans and bond yields
o Assumes period payments are not reinvested
APR = m x km
m = number of periods
km = rate of return or discount rate for one period
Effective annual rate (EAR): compounds the periodic rate the number of times there are periods in the
year
o Assumes periodic payments are reinvested at same rate as original loan
EAR = (1 + km)m 1
MECHANICS OF TIME VALE
Present value: initial investment, also called principle
Future value: principle value plus interest
FV = PV (1+k)
PV = FV / (1+k)
Compound interest: interest earned increases because of interest on interest
o Every year’s ending balance is (1 + discount rate) times the previous year’s balance
FV = PV (1+k)t
PV = FV / (1+k)t
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