# Discount rate

### From Glossary

Also a discount factor. This accounts for the time value of
money and arises naturally in financial models, such as a
portfolio selection problem. A discount rate of
7% means $1 earned a year from now has a *present value* of approximately $93.46
(1/1.07). If $1 is earned n years from now, and the discount rate
is , the present value is $. In continuous-time models,
there are variations, such as defining the present value of
dollars at time to be . In infinite horizon
dynamic programming, the discount factor serves to make
value iteration a contraction map. In
that case, the fixed point of the stationary equation,

is obtained by successive approximation - i.e., value iteration for an infinite horizon DP. This converges to a unique fixed point, , if . Here, the DP notation is used, where is the discount factor.