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

kjcdb8er | Teacher | (Level 1) Associate Educator

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To calculate compounding interest, you at least need to know the interest rate. You also need to know how many times the present day value has been compounded in order to work backwards to the principal. So look at the question for more information from which you can derive these pieces of information.

The simplest form of the equation to calculate compounding interest is A = P( 1 + i )^n, where A is the current amount, P is the principal, i is the rate, and n is the number of times that rate is compounded.

Often, the period of time is in multiples of months (n), with the yearly interest rate (r) being provided. In this case, the rate (i) for the compounding period is i = r/n.

neela | High School Teacher | (Level 3) Valedictorian

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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.