Question

How do you solve A = p + prt for r?

Answer 1

Hint: We are given an equation as A = p + prt. We are asked to solve for r. We will first understand what is given. We will learn about simple interest, its formula and the formula to find the amount. Along with that using the concept of simple interest, we will also solve the above problem without the major concept of simple interest.

Complete step by step answer:
We are given that A = p + prt and we have to solve for r. Before we move further, we need to understand what simple interest is. When we put the amount in a bank, the extra money earned along with the amount we deposit is called Simple Interest. The Simple Interest is given as
\[I=p\times r\times t\]
where p is the principal (initial money), r is the rate of interest and t is the time.
Now, the total amount we get after we keep it say t years is calculated as Amount and is denoted by A. Its formula is the sum of initial money and interest. So,
\[A=p+I\]
As \[I=p\times r\times t\] so we get A as
\[\Rightarrow A=p+p\times r\times t\]
So in our problem, we have been given the amount and we are asked to find the value of the rate of interest r. Now, we have,
\[A=p+prt\]
So, we will first subtract p on both the sides, we get,
\[\Rightarrow A-p=p+prt-p\]
On simplifying, we get,
\[\Rightarrow A-p=prt\]
Now as we have to find the value of r, so we divide both the sides by \[p\times t.\] So, we get,
\[\Rightarrow \dfrac{A-p}{pt}=\dfrac{p\times r\times t}{pt}\]
On simplifying, we get,
\[\Rightarrow r=\dfrac{A-p}{pt}\]

Hence, we get the rate is given as \[\dfrac{A-p}{pt}.\]

Note: Remember to find the value of r, we just need the algebraic tool. We need to isolate the r. To do so we will first separate p and then \[p\times t.\] We do not actually need the proper knowledge of interest and amount. Also, remember we cannot always divide the equation ax = b by ‘a’ always. If ‘a’ is non – zero then only we can divide both sides by ‘a’.