11.27: Chapters 10 - 11- 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?
What if you willhave $2.30 in ten years – in the prior question. What is its Present Value?
Define “Annuity.”
Why are simple Present- and Future-Value factors reciprocals of one another while annuity factors are not?
How are Ordinary Annuities and Annuities Due different?
How does one adjust an Ordinary Annuity in order to make it an Annuity Due?
Give real world examples of Annuities.
How are annuities and perpetuities different from one another?
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.)
What is a “Growth Perpetuity”?
Explain the “Law of Limits.” How does it apply to Perpetuities? (Search Law of Limits online if it helps.)
Simple Future Factors grow at a(n) increasing/decreasingrate. Which is it? Why?
The rate of change in Future Value factors is increasing/decreasing. Which is it? Why?
A mortgage is self-amortizing. Explain.
Over time, interest expense on a mortgage is increasing/decreasing. Which is it? Why?
Over time, a mortgage’s amortization increases ordecreases. Which is it? Why?
You are given an 8% annual rate on a bank Certificate of Deposit, which pays quarterly. What is its Annual Percentage Equivalent Yield?
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.
Over the life of this mortgage, how much interest will there have been – above and beyond the principal payments?
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?
What if this were an Annuity Due?
In the case of a Perpetuity, why is Present Value unaffected by discounting frequencies?
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.
In the prior question, what if “G” were negative 5% (annually)?
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.
What would the future values be in each of the prior two questions?
Besides for the mathematical necessity, why must “R” exceed “G,” in the Perpetuity model? We are assuming here, “normal” economic circumstances.
The Present Value Annuity Factor must have a value greateror lessthan “n × p.” Which is it and why? What about the Future Value Annuity Factor?

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