11.27 Chapters 10 – 11: Review Questions
- 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 will have $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/decreasing rate. 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 or decreases. 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 greater or less than “n × p.” Which is it and why? What about the Future Value Annuity Factor?