Formulae
•
Simple Interest/Simple Discount/Compound Interest
(1)
S
=
P
(1 +
rt
)
Accumulated value at simple interest
(2)
P
=
S
(1

dt
)
Discounted value at simple discount
(3)
S
=
P
(1 +
i
)
n
Accumulated value at compound interest (after
n
periods)
(4)
S
=
P
(
1 +
j
m
m
)
tm
Accumulated value at interest compounded
m
times per year after
t
years
(5)
S
=
P e
j
∞
t
Accumulated value at interest compounded continuously
(6)
j
=
(
1 +
j
m
m
)
m

1
Effective annual rate of interest compounded
m
times per year
(7)
j
=
e
j
∞

1
Effective annual rate of interest compounded continuously
•
Ordinary Simple Annuity
(
n
payments of $1 at perperiod interest rate
i
)
Discounted Value
A
=
value one period before first payment
=
a
n i
=
1

(1 +
i
)

n
i
Accumulated Value
S
=
value immediately after
n
th
payment
=
s
n i
=
(1 +
i
)
n

1
i
•
Ordinary Simple Perpetuity
(with payment
R
)
Discounted Value one period before first payment
A
=
R
i
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•
Amortization Method:
to amortize
A
with
n
periodic payments of
R
at perperiod interest
rate
i
Outstanding balance
B
k
immediately after the
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 Fall '11
 F.Vinette
 Math, Time Value Of Money, $1, effective annual rate

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