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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