Clarification on amortization of constant payments I have found this formula on wikipedia :
$$P=C_k(1+i)^ {(n-k+1)}$$

which describe the constant payment that has to be paid every year ($C_k$ is the part of the initial loan that is extinguished with the $k$ payment) in order to pay off a loan after a period of $ n $ years , all of them at the constant annual interest rate $ i $ .

My problem is that $ 1 + i $ is elevated to $ n-k+1 $ while I expected $k$ because it's the numbers of years passed when the $ k $ payment is done . It seems that the loan is paid inside out , namely starting to pay the interests at the time $n$ on the first year and so on…Am i right?
Let $L$ be the loan amount, then $L=P\frac{1-(1+i)^{-n}}{i}$

The balance at time $t$ is defined as the present value of the remaining payments, 

$B_t=P\frac{1-(1+i)^{-(n-t)}}{i}$

By using the following equations

$I_k+C_k=P$ and $I_k=iB_{k-1}$ where $I_k$ is the interest paid at time $k$ we derive the following equation

$C_k=\frac{P}{(1+i)^{n-k+1}}$ and after a simple rearrangement we arrive at the formula you presented.