Question

Fabina borrows Rs. 12500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who paid more interest and by how much?

Answer 1

Hint:We are going to use two different formulas for finding simple interest and compound interest. And using these formulas we will find the value of interest and then we will see which one has to give more interest and by how much.

Complete step-by-step answer:
Let’s first write the formula for simple interest and compound interest.
$SI=\dfrac{PRT}{100}$
$CI=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$
Now we know the values of P,R,T from the question.
Let’s first find the value of simple interest by using $SI=\dfrac{PRT}{100}$
P = 12500
R = 12
T = 3
Therefore, SI will be,
$\begin{align}
  & \dfrac{12500\times 12\times 3}{100} \\
 & =4500 \\
\end{align}$
The amount of interest paid by Fabina will be 4500.
Next they said that Radha borrows the same amount for the same period ,compounded annually.So we have to find compound interest.
Now, let’s find the value of compound interest by using $CI=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$
P = 12500
R = 10
T = 3
Therefore, CI will be,
$\begin{align}
  & 12500{{\left( 1+\dfrac{10}{100} \right)}^{3}}-12500 \\
 & =12500{{\left( \dfrac{11}{10} \right)}^{3}}-12500 \\
 & =16637.5-12500 \\
 & =4137.5 \\
\end{align}$
The amount of interest paid by Radha will be 4137.5
From this we can say that Fabina has to pay more interest by $4500 – 4137.5 = 362.5$

Note: Here we have used the formula of finding simple interest and compound interest with the help of that we have found the difference between the two interests. Hence, these two formulas must be remembered if one needs to solve this question correctly. And keep in mind that in place of R we have put the value in percentage as we are already dividing it by 100.