# What is the meaning of the discounted process defined from the interest rate process?

Assume a money market has interest rate process $R(t)$. In Shreve's Stochastic Calculus for Finance II, formula (5.2.17) on page 215 defines the discounted process as $$D(t) = e^{-\int_0^t R(s) ds}.$$

Why is $D(t)$ called "discounted" process?

Does it mean that any value at time t times $D(t)$ will give its present value at time $0$?

-
Note that this question is really barely on topic: I guess you're not a professional quant are you? Anyway, a quick answer was enough, but please look at the faq in the future. –  SRKX Mar 27 '13 at 13:09
@SRKX: I have taken a course for the first four chapters of the book by Shreve, and I am learning the rest of the book now. –  Ethan Mar 27 '13 at 13:17
I get that. But the question is trivial; you even guessed the answer inside. So I guess you can see why I say that if you were a professional quant, you wouldn't have asked it. You can accept the answer if you're OK with it. –  SRKX Mar 27 '13 at 13:23
Indeed, $D(t)$ is the discount factor used to compute the present value of a cash flow at time $t$:
$$PV = D(t) \cdot CF_t$$