Bond pricing, compute YTM ... why t not = 2?
A better symbolism might be as follows.

T : periods to maturity from issuance,
t : periods remaining to maturity,
n : periods lapsed

Then t = T - n. 

In your case, because the 1st coupon was paid the day in question, n = 1. T = 2. Thus, t = 2 - 1 = 1 period remaining to maturity. 

You will only discount from the "current" time, in your example the end of year 1, across the remaining periods.