Bond pricing, compute YTM ... why t not = 2? Consider a two-period corporate bond with the following characteristics. The bond was issued at $t = 0$ with face value $FV = 100$ at $t = 2$. In period $t = 1$ and $t = 2$ coupons of $5$ are paid out ($c = 5$). We are in $t = 1$ and the bond issuer has just paid the first coupon. The price of the bond is 101.942.

Suppose that the bond is callable at $101$. The bond issuer is informed by an investment bank that it can issue a new one period zero coupon bond worth $101$ today for a face value of $104.030$ in $t = 2$.What is the yield to maturity on this hypothetical bond?

The eqaution is given by:
$$P_0 : \frac{c}{(1+r)} + \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^t}$$

Where

$c=0$

$FV= 104.03$ 

$P_0 = 101$

$t=2$

And solve for $r$.
But the right answer is all of this above, but $t=1$ .. Why? When they say that $t=2$?
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.