Question

Find the difference between simple interest and compound Interest on ₹\[20000\] at \[8\] p.c.p.a. for \[2\] years.

Answer 1

Hint:
To solve this problem, i.e., to find the difference between simple interest and compound Interest, we will start with finding the simple interest and compound interest by using the respected formulas, and then after taking the difference between them, we will get our required answer.

Complete step by step solution:
We have been given a principal of ₹\[20000,\] rate of \[8\% \] per annum and a time period of \[2\] years. We need to find the difference between simple interest and compound Interest.
So, to find the difference between simple interest and compound Interest. We will first find simple interest and then find compound interest using the formulas mentioned below.
We know that, Simple Interest, $(SI) = \dfrac{{Principal \times Rate \times Time}}{{100}}$
Now, on putting the given values in the above formula, we get
$SI = \dfrac{{2000 \times 8 \times 2}}{{100}}$
$SI = $₹$3200$
Now, we also know that, Compound Interest, $(CI) = \operatorname{P} {(1 + \dfrac{R}{{100}})^n} - \operatorname{P} $
where, P $ = $ Principal
R $ = $ rate
n $ = $ Time period
On putting the values in the above formula, we get
$
  CI = 20000{(1 + \dfrac{8}{{100}})^2} - 20000 \\
  CI = 20000 \times \dfrac{{27}}{{25}} \times \dfrac{{27}}{{25}} - 20000 \\
  CI = 23328 - 20000 \\
$
$CI = $₹$3328$
So, the difference between Simple Interest and Compound Interest $ = 3328 - 3200 \\$
$ = $ ₹\[128\]

Thus, the difference between simple interest and compound Interest on ₹\[20000\] at \[8\] p.c.p.a. for \[2\] years is ₹\[128.\]

Note: Here, in the question, simple interest and compound interest is mentioned. Let us understand about them in detail. So, interest is the cost of borrowing money from a bank or from any person, where the borrower pays some fee to the lender for the loan. Simple interest is based on the principal amount of the loan taken. While compound interest is based on the principal amount and also the interest that adds on it in every time period.