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
THE ANNUITY DUE
Occasionally you may come across the term annuity due. This means an annuity with the first payment due right away, rather than one period in the future as is the case with the annuity certain. Clearly, an annuity due with n + 1 payments at a given interest rate is worth the value of an annuity (at the same rate) with n payments, plus 1, because of the payment of 1 made right away. The annuity due symbol is sometimes a with two dots over it ( ) and called a double-dot. We won t use the annuity due concept in this book, but you should know what it is.
EXAMPLES
Example 5.1
Recall the college fund discussed in the previous chapter. You want to set up a college fund for your 2-year old child. In the previous chapter, we computed that you needed $39,364.63 now to have $100,000 when your child would be 18, assuming you can earn 6% in the meantime. You don t have $39,364.63 now, but you can make a series of annual payments. How much must you pay annually to have the $100,000 for your child?
The present value of the annuity is $39,364.63. The value of an annuity of 1, for 16 years at 6%, is 10.1058953 (taken from the interest tables). The value you need is $39,364.63. Dividing this by the value of an annuity of 1 (10.1058953) gives $3,895.21. This is the amount you must provide each...
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