532A. (a)
FV
n
=
PMT
+
∑

=
t
1
n
0
t
i)
(1
$50,000
=
PMT
+
∑

=
t
1
15
0
t
.07)
(1
$50,000
=
PMT (FVIFA
7%, 15 yr.
)
$50,000
=
PMT(25.129)
PMT
=
$1,989.73. per year
(b)
PV
=
FV
n
PV
=
$50,000 (PVIF
7%, 15 yr.
)
PV
=
$50,000(.362)
PV
=
$18,100 deposited today
(c)
The contribution of the $10,000 deposit toward the $50,000 goal is
FV
n
=
PV(1 + i)
n
FV
n
=
$10,000 (FVIF
7%, 10 yr.
)
FV
10
=
$10,000(1.967)
=
$19,670
Thus only $30,330 need be accumulated by annual deposit.
FV
n
=
PMT
+
∑

=
t
1
n
0
t
i)
(1
$30,330
=
PMT (FVIFA
7%, 15 yr.
)
$30,330
=
PMT [25.129]
PMT
=
$1,206.97 per year
533A. (a)
This problem can be subdivided into (1) the compound value of the
$100,000 in the savings account (2) the compound value of the $300,000
in stocks, (3) the additional savings due to depositing $10,000 per year in
the savings account for 10 years, and (4) the additional savings due to
depositing $10,000 per year in the savings account at the end of years 6
10.
(Note the $20,000 deposited in years 610 is covered in parts (3) and
(4).)
(1)
Future value of $100,000
FV
10
=
$100,000 (1 + .07)
10
FV
10
=
$100,000 (1.967)
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FV
10
=
$196,700
(2)
Future value of $300,000
FV
10
=
$300,000 (1 + .12)
10
FV
10
=
$300,000 (3.106)
FV
10
=
$931,800
(3)
Compound annuity of $10,000, 10 years
FV
10
=
PMT
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 Spring '08
 Ravi
 $140,000, $138,160, $1,206.97, $1,989.73

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