Lifetime Budget Constraint An agent lives for 2 periods, consumes $c$ and saves $s$ at interest rate $r$ in the first period of life from income $y$. In the second period the agent consumes for any savings. We introduce a percentage tax $T^c$ on consumption in both periods where $0 &lt; T^c &lt; 1$. Assuming initially that $T^c_1 = T^c_2$. What is the consumer's lifetime budget constraint?

Answer: $$c_t (1+T^c_1)+ c_{t+1} \frac{1+T^c_2}{1+r} =y_t$$

I don't understand how we can calculate the budget constraint, can anyone help?
This is more easily seen by writing out the budget constraints for periods 1 and 2 separately, and then eliminate the saving $s$. 

In period 1, the agent spends $\left(1+T_1^c \right)\cdot c_1$ on consumption, and saves the rest, so 
$$(1) \qquad \qquad s=y - \left(1+T_1^c \right)\cdot c_1.$$

In period 2, the agents lives on savings (together with interest income), i.e., consumes all the savings, so 
$$(2) \qquad \qquad \left(1+T_2^c \right)\cdot c_2 = (1+r)s,$$ where we multiplied $s$ with $1+r$ because of the interest from period 1 to period 2. 

Now putting the two equations together, we have 
$$
\left(1+T_2^c \right)\cdot c_2 = (1+r)s= (1+r)( y - \left(1+T_1^c \right)\cdot c_1). 
$$
Divide both sides by $(1+r)$ and rearranging the terms, you get the desired result.