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Chapter 9
Time Value of Money
Discussion Questions
9-1.
How is the future value (Appendix A) related to the present value of a single
sum (Appendix B)?
The future value represents the
expected
worth of a single amount, whereas the
present
value represents the current worth.
FV = PV (1 +
I
)
n
future value
(
29
lue
Present va
1
1
FV
PV
+
=
n
i
9-2.
How is the present value of a single sum (Appendix B) related to the present
value of an annuity (Appendix D)?
The present value of a single amount is the discounted value for one future
payment, whereas the present value of an annuity represents the discounted
value of a series of consecutive future payments of equal amount.
9-3.
Why does money have a time value?
Money has a time value because funds received today can be invested to reach
a greater value in the future. A person would rather receive $1 today than $1 in
ten years, because a dollar received today, invested at 6 percent, is worth
$1.791 after ten years.
9-4.
Does inflation have anything to do with making a dollar today worth more than
a dollar tomorrow?
Inflation makes a dollar today worth more than a dollar in the future. Because
inflation tends to erode the purchasing power of money, funds received today
will be worth more than the same amount received in the future.
9-1

Chapter 09: Time Value of Money
9-5.
Adjust the annual formula for a future value of a single amount at 12 percent
for 10 years to a semiannual compounding formula. What are the interest
factors (FV
IF
) before and after? Why are they different?
(
29
Semiannual
3.207
20
n
6%,
i
Annual
106
.
3
10
n
%,
12
i
A
Appendix
FV
PV
FV
IF
=
=
=
=
×
=
The more frequent compounding under the semiannual compounding
assumption increases the future value so that semiannual compounding is worth
.101 more per dollar.
9-6.
If, as an investor, you had a choice of daily, monthly, or quarterly
compounding, which would you choose? Why?
The greater the number of compounding periods, the larger the future value.
The investor should choose daily compounding over monthly or quarterly.
9-7.
What is a deferred annuity?
A deferred annuity is an annuity in which the equal payments will begin at
some future point in time.
9-8.
List five different financial applications of the time value of money.
Different financial applications of the time value of money:
Equipment purchase or new product decision,
Present value of a contract providing future payments,
Future value of an investment,
Regular payment necessary to provide a future sum,
Regular payment necessary to amortize a loan,
Determination of return on an investment,
Determination of the value of a bond.
Chapter 9
Problems
1.
Future value (LO2)
You invest $2,500 a year for three years at 8 percent.
a
.
What is the value of your investment after one year? Multiply $2,500 × 1.08.

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