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LECTURE
I imagine that most of you have had previous exposure to single sum problems and
ordinary annuities, but annuities due and deferred annuities will be new material for most
of you.
Illustration 6-5
can be used to understand how to solve any annuity problem.
It uses
10 sample problems to demonstrate a 4-step solution method that can be used to solve
any of the problems discussed in the appendix.
A. Introduction.
1.
The importance of the
time value of money.
Money has a time value. Time value means that a dollar is worth more now than a
dollar one year from now, because one dollar held today can be invested to earn
interest or some other form of return and thus will be more than one dollar one year
from now.
2.
Accounting
applications of time value concepts:
bonds, pensions, leases,
long-term notes.
3.
Personal
applications of time value concepts:
purchasing a home, planning for
retirement, evaluating alternative investments.
B. Nature of Interest.
1.
Interest
is payment for the use of money.
It is the excess cash received or
repaid over and above the
principal
(amount lent or borrowed).
2.
Interest rates are generally stated on an
annual
basis unless indicated
otherwise.
3.
Choosing an appropriate interest rate:
a.
is not always obvious.
b.
three components of interest:
(1)
pure rate of interest (2%–4%).
(2)
credit risk rate of interest (0%–5%).
(3)
expected inflation rate of interest (0%–?%).
C. Simple Interest.
Review Illustration 6-1
to distinguish between simple interest and compound interest.
1.
Simple interest
is computed on the amount of the principal only.
2.
Simple interest =
p
x
i
x
n
where
p
= principal.
i
= rate of interest for a single period.
n
= number of periods.
D. Compound Interest.
1.
Compound interest
is computed on the principal
and
on any interest earned
that has not been paid or withdrawn.
2.
The power of
time
and
compounding.
(E.g., “What do the numbers mean?” on
text page 255 indicates that at 6% compounded annually, $24 grows to $79
billion in 376 years.
At 6% simple interest, $24 would grow to only $565.44 in
376 years.)
$565.44 = $24 + ($24 x .06 x 376).
3.
The term
period
should be used instead of
years.
a.
Interest may be compounded more than once a year:
If interest is
Number of compounding
compounded
periods per year

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Annually
1
Semiannually
2
Quarterly
4
Monthly
12
b.
Adjustment when interest is compounded more than once a year.
(1)
Compute the compounding period
interest rate:
divide
the annual
interest rate by the number of compounding periods per year.
(2)
Compute the total number of compounding
periods:
multiply the
number of years by the number of compounding periods per year.
E. Terminology Used in Compound Interest Problems.
1.

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