Question

The C.I. on a certain sum for $2$ years is Rs $410$ and S.I. is Rs $400.$ What is the rate of interest per annum?

• A. $10\%$
• B. $8\%$
• C. $5\%$
• D. $4\%$

Answer 1

Answer: (C)

$5\%$

$\Rightarrow$ It is given that simple interest in 2 years = Rs.400

$\Rightarrow$ Simple interest for 1 year = Rs.200

$\Rightarrow$ Hence, Compound interest for 1 year = Rs.200

$\Rightarrow$ Given compound interest for 2 years = Rs. 410

$\therefore$ Compound interest for 2 years = Compound interest 1st year + Compound interest 2nd year

$\Rightarrow$ Compound interest for 2nd year = Rs.410 - Rs.200 = Rs.210

$\Rightarrow$ That is interest on Rs.200 for 1 year = Rs.210-Rs.200=Rs.10

$\Rightarrow$ We know $I=\frac{P\times T\times R}{100}$

$\Rightarrow$ $10=\frac{200\times 1\times R}{100}$

$\Rightarrow$ $2R=10$

$\therefore$ $R=5\%$