Jessica Chung & Sri Muhunthan
Week 05
QMA PASS  2006 S1  Mon, 121pm  WEB 251
Questions? Email us: [email protected]
, [email protected]
1/4
G
EOMETRIC
P
ROGRESSIONS
(1
)
1
k
a
r
S
r

=

for r < 1
(
1)
1
k
a r
S
r

=

for r > 1
A
NNUITIES
An annuity is:
°
a number of equal
payments
°
made at regular
intervals
°
over a fixed
term
O
RDINARY
A
NNUITY
An ordinary annuity assumes that regular payments are made at the END
of a period.
Present Value of an Ordinary Annuity
1
(1
)
n
i
P
R
i

°
±

+
²
³
=
×
E
XAMPLE
What is the present value of a 10year series of $1000 monthly payments assuming an interest rate of 7.2%
per annum compounding monthly?
t = 10
k = 12
r = 7.2%
R = $1000
(
)
120
7.2%
1
(1
)
12
$1000
7.2%
12
$85,366.57
P

°
±

+
´
µ
²
³
=
×
=
Future Value of an Ordinary Annuity
(1
)
1
n
n
i
S
R
i
°
±
+

²
³
=
×
E
XAMPLE
Calculate the future value of the series of money in the above question.
t = 10
k = 12
r = 7.2%
R = $1000
(
)
120
7.2%
(1
)
1
12
$1000
7.2%
12
$175,003.01
S
°
±
+

´
µ
²
³
=
×
=
A
NNUITIES
D
UE
An annuity due assumes that regular payments are made at the BEGINNING
of a period.
Present Value of an Annuity Due
1
(1
)
(1
)
n
R
i
P
r
i

°
±

+
²
³
=
+
×
E
XAMPLE
If interest were paid at the beginning of a period, calculate the present value of the above stream of money.
t = 10
k = 12
r = 7.2%
R = $1000
(
)
(
)
120
7.2%
$1000 1
(1
)
12
7.2%
1
12
7.2%
12
$85,878.77
P

°
±

+
´
µ
²
³
=
+
×
=
Future Value of an Annuity Due
(1
)
1
(1
)
n
n
R
i
S
i
i
°
±
+

²
³
=
+
×
E
XAMPLE
If the above annuity was an annuity due, calculate the future value of the payment stream.
t = 10
k = 12
r = 7.2%
R = $1000
(
)
(
)
120
7.2%
$1000 (1
)
1
12
7.2%
1
12
7.2%
12
$176,053.03
S
°
±
+

´
µ
²
³
=
+
×
=
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Jessica Chung & Sri Muhunthan
Week 05
QMA PASS  2006 S1  Mon, 121pm  WEB 251
Questions? Email us: [email protected]
, [email protected]
2/4
S
INKING
F
UND
A sinking fund is a fund into which regular payments are made in order to achieve a specific objective in the future (such as to replace a machine or a
car). You can think of it as if you were depositing this money into the bank (ie just an ordinary annuity type problem) for a holiday abroad.
E
XAMPLE
:
Derek wants to establish a fund for his Jag of $300,000. He needs to pay an equal amount at the end of each quarter for 10 years, the interest rate is
8% p.a. compounded quarterly.
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 Three '08
 julia
 Time Value Of Money, Debt, Mortgage loan, Jessica Chung

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