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Calculating Ordinary Annuity
Number of payments is equal to the number of interest periods.

Calculating Annuity Due
Number of interest periods is one less than the number of payments

Present Value of an ordinary annuity
The present value of an ordinary annuity is the current worth of a series of identical periodic payments to be made in the future.
 EX:
 Periodic Lease payments
 Periodic Bond Payments
 Winning the lottery

Future value of ordinary annuity is the sum, to be received at some point in the future, identical periodic invesments made from the present until that future point.
The future value of an ordinary annuity

Present value and future value of annuity due
The only difference in the calculations of an annity due and an ordinary annuity is the timing of the payments. Therefore, by adding 1 to the present value of an oridnary annuity of 1 for n periods, the present value of an annuity due of 1 for n+1 periods may be found.

