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11.27: Chapters 10 - Review Questions
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You are given $2.30 in the present. It will compound quarterly at annual rate of 12% for ten years. What is its Future Value?
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What if
you
will
have
$2.30 in ten years – in the prior question. What is its Present Value?
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Define “Annuity.”
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Why are simple Present- and Future-Value factors reciprocals of one another while annuity factors are not?
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How are Ordinary Annuities and Annuities Due different?
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How does one adjust an Ordinary Annuity in order to make it an Annuity Due?
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Give
real world
examples of Annuities.
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How are annuities and perpetuities different from one another?
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An annuity due pays $138
.55
every quarter for seven years at a rate of 4.375%. Calculate both its present- and future-values. (
Hint
: use the mathematical formula for calculating annuity factors and also use the annuity adjustment multiplier.)
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What is a “Growth Perpetuity”?
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Explain the “Law of Limits.” How does it apply to Perpetuities? (Search Law of Limits online if it helps.)
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Simple Future Factors grow at a(n)
increasing/
decreasing
rate
. Which is it? Why?
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The rate of change in Future Value factors is
increasing/decreasing
. Which is it? Why?
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A mortgage is self-amortizing. Explain.
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Over time, interest
expense
on a mortgage is
increasing/decreasing
. Which is it? Why?
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Over time, a mortgage’s amortization
increases
or
decreases
. Which is it? Why?
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You are given an 8% annual rate on a bank Certificate of Deposit, which pays quarterly. What is its Annual Percentage Equivalent Yield?
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A mortgage charges 5% interest payable annually for thirty years. How much interest and amortization will there be in the second year? Assume a loan of $1 million.
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Over the life of this mortgage, how much interest will there have been – above and beyond the principal payments?
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An investor will receive a $400, 4% annual annuity for the next ten years, payable semi-annually; that is $200 every six months. What
are
the present- and future values of the
annuity?
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What if this were an Annuity Due?
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In the case of a Perpetuity, why is Present Value unaffected by discounting frequencies?
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A semi-annual, “constant-growth” cash flow series last paid, $5.80. Payments will be made every six months and will grow at an annual rate of10% per year. Assume a four-year horizon. What is the Present Value of the cash flow series?Utilize a 12% discount rate.
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In the prior question, what if “G” were negative 5%
(annually)
?
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A Perpetuity last paid $1.50. It will be discounted at an annual rate of 16% and its cash flow will grow at an annual rate of 8% to be paid in quarterly installments. What is its Present Value? Be sure to adjust for frequencies.
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What would the future values be in each of the prior two
questions?
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Besides for the mathematical necessity, why must “R” exceed “G,” in the Perpetuity model?
We are assuming here, “normal” economic circumstances.
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The Present Value Annuity Factor must have a value
greater
or
less
than
“n × p.” Which is it and why? What about the Future Value Annuity Factor?