Editing Present value (section)

==Background==
If offered a choice between $100 today or $100 in one year, and there is a positive real interest rate throughout the year, a rational person will choose $100 today. This is described by economists as [[time preference]]. Time preference can be measured by auctioning off a risk free security—like a US Treasury bill. If a $100 note with a zero coupon, payable in one year, sells for $80 now, then $80 is the present value of the note that will be worth $100 a year from now. This is because money can be put in a bank account or any other (safe) investment that will return interest in the future.

An investor who has some money has two options: to spend it right now or to save it. But the financial compensation for saving it (and not spending it) is that the money value will accrue through the [[compound interest]] that he or she will receive from a borrower (the bank account in which he has the money deposited).

Therefore, to evaluate the real value of an amount of money today after a given period of time, economic agents compound the amount of money at a given (interest) rate. Most [[Actuarial science|actuarial]] calculations use the [[risk-free interest rate]] which corresponds to the minimum guaranteed rate provided by a bank's saving account for example, assuming no risk of default by the bank to return the money to the account holder on time. To compare the change in purchasing power, the [[real interest rate]] ([[nominal interest rate]] minus [[inflation]] rate) should be used.

The operation of evaluating a present value into the [[future value]] is called a capitalization (how much will $100 today be worth in 5 years?). The reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much will $100 received in 5 years—at a lottery for example—be worth today?).

It follows that if one has to choose between receiving $100 today and $100 in one year, the rational decision is to choose the $100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least $105 in one year so that the two options are equivalent (either receiving $100 today or receiving $105 in one year). This is because if $100 is deposited in a savings account, the value will be $105 after one year, again assuming no risk of losing the initial amount through bank default.