Fixed Income Mathematics
Offering explanations, exercises, and examples without demanding sophisticated mathematics, this self-teaching book will serve as a gateway to financial mathematics and to increased competence in business analysis.
TABLE OF CONTENTS Fixed Income Mathematics
CHAPTER SUMMARY
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An annuity certain is a series of equal payments, equally spaced in time, starting in one period.
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Life annuities have a life contingency factor and are not annuities certain.
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The equation for an annuity certain with n payments is
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To solve for the interest rate, given the annuity certain and its cost, use the bisection method discussed earlier or some other numerical analysis approach.
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Annuities certain are important in finance, especially in figuring and scheduling loan repayments. Scheduled loan repayments are good financial policy for both borrower and lender.
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For the annuity certain equation to hold, all the payments must be the same, they must all be evaluated at the same interest rate, and the time periods between the payments must all be the same.
COMPUTER PROJECT
For a range of interest rates, say 1% to 30%, compute the values of a perpetuity, an annuity certain for 100 years, and the difference. How much would you pay to convert a 100-year annuity certain to a perpetuity? What is the difference between the calculated value and the amount you would pay? What, if anything, does this tell you about the psychology of markets?
TOPICS FOR CLASS DISCUSSION
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You are retiring at age 60 with a pension of $1,500 monthly. You can receive a Social Security pension of $1,100 monthly, starting in 2 years. Your human resources department has offered to pay you an increased pension for 2 years, until your Social Security payments start, and then a reduced...
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