Annuity and Settlements

What are annuities, and why is it necessary to calculate their present value? Why is the calculation of the present value of any future amount important? Why is the present value of any future amount greater when the discount rate is lower? Explain your

Annuity is an amount of money given to you at fixed interval for an infinite amount of time (assuming you lived that long).
Well, the discount rate is closely linked to two factors: normal interest rate and inflation rate.
So an amount in the future, say $100, a year from now with an inflation rate of 10%, when discounted to the present, would just be about $90. (e.g 100 bucks in the future can only buy an equivalent 90 bucks of goods now) So you can imagine if the discount rate is 5%, the present value would be about $95.
The calculation of present value is important because it provides for a basis of comparison of money at different times. Say $1000 in 20 years time is definitely not the same as $1000 now. So by discounting the amount to its present value, we could then differentiate their worth.
Hope this helps.