Question

Question 1

Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities
(i) C >S
(ii) C =S
(iii) C < S
Then,
(a) only (i) is correct
(b) either (i) or (ii) correct
(c) either (ii) or (iii) is correct
(d) only (iii) is correct

Answer 1

Let the principal (P) = Rs 100
Rate of interest (R) = 10%
and time period (T) = 1 yr
Then, simple interest $=\frac{P\times R\times T}{100}=\frac{100\times 10\times 1}{100}=Rs.10$
We know that,
$A=P{(1+\frac{R}{100})}^r=100{(1+\frac{10}{100})}^1=100\times \frac{11}{10}=Rs.110$
$\therefore$ Compound interest, CI = A - P = Rs.110 - Rs. 100 = Rs. 10
So, C =S
Hence, option (ii) is possible.

Now
Let the principal (P) = Rs 100
Rate of interest (R) = 10%
and time period (T) = 2 yr
Then, simple interest $=\frac{P\times R\times T}{100}=\frac{100\times 10\times 2}{100}=Rs.20$
We know that,
$A=P{(1+\frac{R}{100})}^r=100{(1+\frac{10}{100})}^2=100\times \frac{11}{10}\times \frac{11}{10}=Rs.121$
$\therefore$ Compound interest, CI = A - P = Rs.121 - Rs. 100 = Rs. 21
So, C >S
Hence (i) is also possible.
Therefore (b) is the correct option.