Question

A sum of Rs. 2400 is invested at 15% per annum for 2 years compounded annually. Find the compounded interest and also the difference between the simple and the compound interest.

Answer 1

Hint: With the given information, we can calculate simple interest (SI) and compound interest (CI) using:
$SI = \dfrac{{P \times R \times T}}{{100}}$
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$ where
P = Principal
R = Rate
T = Time
A = Amount.
Relationship of interest with amount and principal:
Amount (A) = Principle (P) + Interest (CI)
CI = A – P ____ (1)

Complete step-by-step answer:
Given:
Principal (P) = Rs. 2400
Rate (R) = 15 %
Time (T) = 2 years
Now,
i) The simple interest (SI) is given as:
$\Rightarrow SI = \dfrac{{P \times R \times T}}{{100}}$
Substituting the respective values, we get:
$\Rightarrow SI = \dfrac{{2400 \times 15 \times 2}}{{100}}$
SI = 720
Thus the value of simple interest is Rs. 720.
ii) The amount (A) for compound interest can be calculated as:
$\Rightarrow A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
Substituting the respective values, we get:
$
\Rightarrow A = 2400{\left( {1 + \dfrac{{15}}{{100}}} \right)^2} \\
\Rightarrow A = 2400 \times \dfrac{{115}}{{100}} \times \dfrac{{115}}{{100}} \\
 $
A = 3174
From (1),
CI = A – P
Substituting the values:
$\Rightarrow$ CI = 3174 – 2400
$\Rightarrow$ CI = 774
Thus the value of compound interest is Rs. 774.
The difference between CI and SI can be given as:
$\Rightarrow$ D = CI – SI
$\Rightarrow$ D = 774 – 720
$\Rightarrow$ D = 54
Therefore, the compounded interest is Rs. 774 and the difference between CI and SI is Rs. 54

Note: In compound interest, the amount can be found by adding the interests obtained in subsequent years in principle as well but this method is more error-prone. It is always better to use the mentioned formula.
CI along with compounded annually can also be compounded half-yearly and quarterly. In case of half-yearly, the rate gets reduced to half whereas the time gets doubled