When forming the budget constraint for the intertemporal utility function $\displaystyle U_t=lnc_t + \frac{1}{1+\rho}lnc_{t+1}$, given that there is labour income in period 1 in the amount $\displaystyle w_t$ and interest on savings from the first period at rate $\displaystyle 1+r$, should the interest income be discounted? That is, should the budget constraint be

$\displaystyle

c_t + \frac{c_{t+1}}{1+r} \leq(1-s)w_t + sw_t(1+r)

$

(where s is savings, c is consumption)

OR:

$\displaystyle

c_t + \frac{c_{t+1}}{1+r} \leq (1-s)w_t + sw_t(1+r)/(1+r)

$

The second makes better theoretical sense (both sides of the equation are in PV terms), but my professor claims the first one is correct. I'm at a loss.