7 rear cogs and a 300EX rear derailleur point to your bike being from 1994.

http://www.bikepedia.com/QuickBike/B...igee&Type=bike

1994 Giant Perigee
Bicycle Type Road/sport
MSRP (new) $370.00
Weight 25.0
Sizes 52, 54, 56, 58, 60
Colors
Item ID 17074

Frame & Fork
Frame Construction Lugged steel
Frame Tubing Material Chromoly
Fork Brand & Model Chromoly, unicrown
Fork Material
Rear Shock

Components
Component Group Shimano 300EX
Brakeset Shimano A250 brakes, levers
Shift Levers Shimano 400EX down-tube
Front Derailleur Shimano 300EX
Rear Derailleur Shimano 300EX
Crankset Shimano 300 EX, 40/52 teeth
Pedals SR/Suntour Road
Bottom Bracket
BB Shell Width
Rear Cogs 7-speed, 13 - 26 teeth
Chain Sedis
Seatpost Kalloy alloy
Saddle Giant Road
Handlebar Steel with alloy Sleeve
Handlebar Extensions
Handlebar Stem SR 90 Degree Bend
Headset

Wheels
Hubs Alloy
Rims Araya SP-30, 36-hole
Tires Giant
Spoke Brand
Spoke Nipples