Question

Suppose for the principal P, rate R%, and time T years the simple interest is S and compound interest is C. Consider the possibilities:-
 (i) C > S (ii) C = S (iii) C < S
Which of the following options hold?
A) Only (i) is correct.
B) Either (i) or (ii) is correct.
C) Either (ii) or (iii) is correct.
D) Only (iii) is correct.

Answer 1

Hint: The following two are the formulas which would be used in solving the question
SIMPLE INTEREST = \[\dfrac{P\times R\times T}{100}\].
COMPOUND INTEREST AMOUNT \[=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\].
We will solve this question by taking two examples.

Complete step-by-step answer:
Let us take an example:-
Say, Principal = Rs. 2500; Rate = 10%; Time = 2 years
SIMPLE INTEREST (S)
The formula to find Simple Interest is:-
Simple Interest = \[\dfrac{P\times R\times T}{100}\]
Therefore, Simple Interest \[=\dfrac{2500\times 10\times 5}{100}\] .
  Simple Interest = 1250
As Simple Interest is Rs. 1250, the amount will be (Simple Interest + Principal Amount).
Therefore, Amount = (1250 + 2500) = Rs. 3750
COMPOUND INTEREST (C)
The formula to find Compound Interest is:-
Amount \[=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
Therefore, Amount
 \[\begin{align}
  & =2500{{\left( 1+\dfrac{10}{100} \right)}^{5}} \\
 & =2500{{\left( \dfrac{11}{10} \right)}^{5}} \\
 & =4026.27 \\
\end{align}\]
Therefore, Amount = Rs. 4026.27
Let us take another example:-
Say, Principal = Rs.160; Rate = 5%; Time = 3 years
SIMPLE INTEREST (S)
Simple Interest = \[\dfrac{160\times 5\times 3}{100}\]
Simple Interest = 24
As the Simple Interest is Rs. 24, amount will be (Simple Interest + Principal Amount).
Therefore, Amount = (24 + 160) = Rs. 184
COMPOUND INTEREST (C)
Amount \[=160{{\left( 1+\dfrac{5}{100} \right)}^{3}}\]= Rs. 185.22
Therefore, Amount = Rs.185.22
After solving these two examples, we can observe the following:-
Example 1:-
Simple Interest Amount = Rs.3750
Compound Interest Amount = Rs.4026.27
Example 2:-
Simple Interest Amount = Rs.184
Compound Interest Amount = Rs.185.22
In example 1, we can observe that Compound Interest Amount is more than the Simple Interest Amount.
In example 2 also, we can observe that Compound Interest Amount is more than the Simple Interest Amount.
Therefore, we can conclude that the Amount of Compound Interest is always more than the Amount of Simple Interest.
Hence, the answer of the question is (a) Only (i) is correct.

Note: One must always remember the formulas to find Simple Interest and Compound Interest.
SIMPLE INTEREST = \[\dfrac{P\times R\times T}{100}\].
COMPOUND INTEREST AMOUNT \[=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\].