How do you find the principal without time or rate when calculating compounding interest?

The cost of the money  per unit amount of money for a fixed period (normally one year) is the the rate of interest (r) . If a Principal amount P is invested at the rate of interest r  compounding period every year,for a period T, then the amount A we get  after the period T is given by the formula:

A= P(1+r)^T. (1)

The nominal rate of interest may have to be converted proportionally to the periodicity of compounding.

Now look at the formula at one. You want to get the the principal P.Then we can  modify the  above formula under the rules of equation  to obtain P as below:

P=A*(1+r)^(-T)  or  P=A/(1+r)^T.       (2)

Therefore, to get P on the left, you must know, A ,r and T on the right side. Otherwise, it remains only an algebraic formula as to how to get P from the symbols A,r andT.

O shall I say the above formula  at (2) itself is an answer, as you have not given any information about period , rate of interest and amount.