    # Present Value � Annuity An annuity is a series of equal annual cash flows. In general terms, the present value of an annuity may be expressed as follows:

 PV An = A A A + + ........ (1 + r)1 (1 + r)2 (1 + r)n
OR
 PV An = A { ∑ n      1 / (1 + r)t } t = 1
 Where PV An = Present value of an annuity A = annuity amount (even cash inflows) r = discount rate and n = number of years of annuity (the last year)

Example: Let us find out the present value of an annuity of \$10,000 to be received in the next 4 years time, the discount rate being 10%.

 Years Cash inflows PV factor at 10% PV of cash inflows 1 \$10,000 0.9091 \$9,091 2 \$10,000 0.8264 \$8,264 3 \$10,000 0.7513 \$7,513 4 \$10,000 0.6830 \$6,830 Total \$31,698.00

Graphic Presentation of Time Line of Present value of Annuity

 0 1 2 3 4 \$ 10,000 \$ 10,000 \$ 10,000 \$ 10,000 \$ 10,000 \$ 9,091 \$ 8,264 \$ 7,513 \$ 6,830 \$ 31,698 (Total PV)

Alternatively, the PV of an annuity can also be calculated by the formula:

 PV An = A [ { 1 - (1/ (1 + r))n } / r ]

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