The manufacture date is stamped in the barrel on the left side close to the Remington action. The year code does rotate, so it's still nice to know the approximate age. Here's the pdf on serial numbers, but it doesn't have everything listed. Blue Book of Gun Values - Firearm Serialization
I say that's not true because you are certainly capable of reading the markings on the firearm and posting what you find. (That'll tell us the model and chambering, among other things.) You also know how long you have had it so you know it must be older than a certain age. You know where you got it and can tell us about that. For example, if you bought it as a new firearm in a gun store 5 years ago, then we have a pretty good idea that it's about 5 years old. If you tell us it's been sitting in a closet the whole time since then, we'll have a pretty good guess about the condition. Combine all that with a model number (engraved on the firearm, somewhere) and the smart folks around here can probably provide you with a reasonably accurate range of values.
I assume, of course, that you're willing to do that small amount of work, at minimum, to maximize your return.
That would be a model 740. When you next have access to it, read everything engraved on it and post back. Then post some good closeup pictures. We're certainly willing to help you figure out what you've got.