To conclude this comparison of present and future values, compare Figures A.1 and A.2.2


An annuity is defined as a series of payments of a fixed amount for a specified number of periods. Each payment occurs at the end of the period.3 For example, a promise to pay $1,000 a year for 3 years is a 3-year annuity. If you were to receive such an annuity and were to deposit each annual payment in a savings account paying 4% interest, how much would you have at the end of 3 years? The answer is shown graphically as a time line in Figure A.3. The first payment is made at the end of year 1, the second at the end of year 2, and the third at the end of year

Notice that Figure A.2 is not a mirror image of Figure A.1. The curves in Figure A.1 approach <» as n increases; in Figure A.2 the curves approach zero, not —».

Had the payment been made at the beginning of the period, each receipt would simply have been shifted back

1 year. The annuity would have been called an annuity due; the one in the present discussion, with payments made at the end of each period, is called a regular annuity or, sometimes, a deferred annuity.

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