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Managerial Economics (ARE) 144
University of California, Davis
Instructor: John H. Constantine
UPDATED ON 4/13/11.
KEY—Handout: Chapter 3, The Interest Factor in Financing
(1)
What is the essential concept in understanding compound interest?
The concept of earning interest on interest is the essential idea that must be understood in the
compounding process and is the cornerstone of all financial tables and concepts in the mathematics of
finance.
(2)
What general rule can be developed concerning maximum values and compounding intervals within a
year? What is an equivalent annual yield?
Whenever the nominal annual interest rates offered on two investments are equal, the investment with
the more frequent compounding interval within the year will always result in a higher effective annual
yield. An equivalent annual yield is a single, annualized discount rate that captures the effects of
compounding (and if applicable, interest rate changes).
(3)
What does the time value of money (TVM) mean?
Time value simply means that if an investor is offered the choice between receiving $1 today or receiving
$1 in the future, the proper choice will always be to receive the $1 today, because that $1 can be invested
in some opportunity that will earn interest. Present value introduces the problem of knowing the future
cash receipts for an investment and trying to determine how much should be paid for the investment at
present. When determining how much should be paid today for an investment that is expected to
produce income in the future, we must apply an adjustment called discounting to income received in the
future to reflect the time value of money.
(4)
How does discounting, as used in determining present value, relate to compounding, as used in
determining future value? How would present value ever be used?
The discounting process is a process that is the opposite of compounding. To find the present value of
any investment is simply to compound in a “reverse” sense. This is done by taking the reciprocal of the
interest factor for the compound value of $1 at the interest rate, multiplying it by the future value of the
investment to find its present value. Present value is used to find how much should be paid for a
particular investment with a certain future value at a given interest rate.
(5)
Why can’t interest factors for annuities be used when evaluating the present value of an uneven series
of receipts?
What factors must be used to discount a series of uneven receipts?
With an annuity, interest factors can be summed because the payments are equal in amount
and
are
received at equal intervals. If the series of annuities being evaluated is uneven, the interest factors
cannot be summed and the interest factors for annuities are of value mathematically. In the case of an
uneven series of receipts, the calculation requires the use of individual ordinary present value factors.
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This note was uploaded on 03/14/2012 for the course ARE 144 taught by Professor Johnson,e during the Spring '08 term at UC Davis.
 Spring '08
 Johnson,E

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