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
ANALYSIS AND CALCULATION OF SOME COMBINATION ANNUITIES CERTAIN
Sometimes you may have a problem that requires you to calculate the present value of part of an annuity certain. You may be able to compute the required value by analyzing the flow of funds and splitting it up into several annuities certain or expressing it in some combination of annuities certain. Here are two examples.
Example 5.5
You are receiving an annuity of 2 for 10 years, and then an annuity of 1 for 10 additional years. Using i = 6%, what is the value of your annuity?
Split your series of payments into an annuity of 1 for 10 years and an annuity of 1 for 20 years. Adding these two annuities together will give you your annuity. An annuity of 1 for 10 years at 6% is 7.36008705. An annuity of 1 for 20 years at 6% is 11.4699212 (both values from the table). Adding these together gives 18.83000825. This is the value of your annuity.
Example 5.6
You will receive an annuity of 1 for 10 years starting 11 years from now and ending 20 years from now. Using a 6% interest rate, what is the present value of your annuity?
You can compute the present value by taking the value of a 20-year annuity and deducting from it the value of a 10-year annuity, representing the payments you will not be receiving. The 20-year value is 11.4699212, and the 10-year value is 7.36008705 (both values from...
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