CHAPTER 5
The Time Value of Money
Homework Solutions
ANSWERS TO
ENDOFCHAPTER QUESTIONS
51.
The concept of time value of money is recognition that a dollar received today is
worth more than a dollar received a year from now or at any future date.
It exists
because there are investment opportunities on money, that is, we can place our dollar
received today in a savings account and one year from now have more than a dollar.
52.
Compounding and discounting are inverse processes of each other.
In compounding,
money is moved forward in time, while in discounting money is moved back in
time.
This can be shown mathematically in the
compounding equation:
FV
n
=
PV (1 + i)
n
We can derive the discounting equation by multiplying each side of
this equation by and we get:
PV
=
FV
n
53.
We know that
FV
n
=
PV(1 + i)
n
Thus, an increase in i
will increase FV
n
and a decrease in n
will
decrease FV
n.
54.
Bank C which compounds daily pays the highest interest.
This occurs because,
while all banks pay the same interest, 5 percent, bank C compounds the 5 percent
daily.
Daily compounding allows interest to be earned more frequently than the
other compounding periods.
55.
The values in the present value of an annuity table (Table 58) are actually derived
from the values in the present value table (Table 54).
This can be seen, by
examining the values represented in each table.
The present value table gives values
of
for various values of i and n, while the present
value of an annuity table gives
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values of
∑
=
+
n
1
t
t
i)
(1
1
for various values of i and n.
Thus the value in the present value of annuity table for
an n
year annuity for any discount rate i
is merely the sum of the first n
values in the
present value table.
PVIFA
10%,10yrs
=
6.145.
∑
=
10
1
n
PVIF10%,n = 6.144 = 0.909 +
0.826 + 0.751 + 0.683 + 0.621 + 0.564 + 0.513 + 0.467 + 0.424 + 0.386
56.
An annuity is a series of equal dollar payments for a specified number of years.
Examples of annuities include mortgage payments, interest payments on bonds,
fixed lease payments, and any fixed contractual payment.
A perpetuity is an annuity
that continues forever, that is, every year from now on this investment pays the same
dollar amount.
The difference between an annuity and a perpetuity is that a
perpetuity has no termination date whereas an annuity does.
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 Spring '10
 LIbnitz
 Finance, Time Value Of Money

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