ORIE 350
Homework #7
Time Value of Money
1.
Alex Trabeck opens a savings account at CFCU.
The advertised APR is 3.45%,
compounded monthly.
If he deposits $20,000 today, what will the balance be in the
account 30 months from now, assuming no other deposits or withdrawals?
(
29
(
29
002831
.
0
1
0345
.
1
1
1
12
1
1
=

=

+
=
c
APR
i
(
29
(
29
89
.
769
,
21
$
002831
.
1
000
,
20
1
30
=
=
+
=
n
i
PV
FV
2.
You have just made a $10,000 deposit to your savings account.
Your rich aunt will
make an additional deposit of $8,000 to your account one year from now.
Assuming you
earn an annual nominal interest rate of 4%, compounded monthly, and make no
additional contributions, what will your account be worth 4 years from today?
The $10,000 deposit earns interest for 48 months; the $8,000 deposit earns interest for
36 months.
The interest rate per month is 0.04/12 = 0.003333.
(
29
(
29
(
29
n
48
36
FV
PV 1 i
10,000 1.003333
8,000 1.003333
$20,750.16
=
+
=
+
=
3.
An investment pays you 15 annual payments of $40,000, with the first payment
occurring 11 years from now.
Recall that the compounding frequency equals the
payment frequency unless explicitly stated otherwise.
a.
If the annual nominal interest rate is 7%, then what is the value of the investment
today?
(
29
(
29
n
15
10
1
1 i
1
1.07
PV
A
40,000
$364,316.56
i
0.07



+

=
=
=
(
29
10
0
10
PV
PV
$185,200.07
1.07
=
=
b.
What is the value of a similar investment, with identical terms except the annuity
extends for 20 years, instead of 15 years?
(
29
(
29
n
20
10
1
1 i
1
1.07
PV
A
40,000
$423,760.57
i
0.07



+

=
=
=
(
29
10
0
10
PV
PV
$215,418.39
1.07
=
=