Question

In the equation$i = prt$, Solve for$p$.

Answer 1

We know that $i = prt$is the simple interest formula where:
$i$= interest amount

$p$= principal amount

$r$= rate of interest per year

$t$= time periods involved

So in the above given equation we have to solve for $p$, which can be found by isolating the $p$ term from all other terms which can be achieved either by dividing or multiplying a common factor on both sides of the given expression. Thus we can find an expression for $p$ alone.

Complete step by step solution:
Given
$i = prt.............................\left( i \right)$

Now from (i) we have to get the expression for $p$i.e. for the principal amount. Now for solving
$p$from the simple interest formula we have to eliminate all the terms along with $p$in such a way that the equation remains still unchanged.

This can be done only by dividing a common term on both sides of the equation such that the equation remains mathematically correct.

Since we have to find expression for $p$ we have to eliminate all those factors that are with the
term$p$.

Also the term present with $p$is$rt$.

So dividing both the LHS and RHS of the equation (i) with$rt$.

Therefore (i) becomes:
$\;\;\dfrac{i}{{rt}} = \dfrac{{prt}}{{rt}} \\\ \Rightarrow \dfrac{i}{{rt}} = p \\\ \Rightarrow p = \dfrac{i}{{rt}}.................\left( {ii} \right) \\\$
So (ii) represents the expression of $p$from $i = prt$ .

Therefore $p = \dfrac{i}{{rt}}$is our required answer.

Note: $p$or the principal amount is simply the total amount of money that one borrows.
Also in questions where we have to find the equation for a variable the above approach is considered since it’s simple and easy to follow. Also the equation (ii) is quite important in questions for calculating interests and principal amount.