Two years compound interest at rate of 10% per annum for an amount is Rs 420/- What will be the simple interest for 3 years for the same amount at the same rate.

Correct option is C

Given:
Compound Interest for 2 years = ₹420
Rate = 10% per annum
Time for Simple Interest = 3 years
Same principal and rate used for both CI and SI

Formula Used:

​$$A = P \left(1 + \frac{R}{100}\right)^T$$​​

Simple Interest (SI) = $$\frac{P \times R \times T}{100}$$

Compound interest (CI) = A - P​​

Where:
A is the amount after interest.
P is the principal.
R is the rate of interest per annum.
T is the time in years.

Solution:

CI = A - P

​$$CI = P \left(1 + \frac{R}{100}\right)^T - P$$​​

​$$CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]$$​
$$420 = P \left[\left(1 + \frac{10}{100}\right)^2 - 1\right]$$​​

​$$420 = P \left[\left(1.1\right)^2 - 1\right]$$​​

$$420 = P \left[1.21 - 1\right]$$​​

​$$420 = P \times 0.21$$​​

​$$P = \frac{420}{0.21}$$​​

P = 2000

Simple interest on 3 years;

​$$SI = \frac{2000 \times 10 \times 3}{100}$$​​

​$$SI = \frac{60000}{100}$$​​

SI = 600

So, the simple interest for 3 years is Rs. 600.

Thus, the correct answer is (c).

Alternative Method:

Interest 10%;

21x² = 420

x² = $$\frac{42}{21} = 20$$​​

Principle = 100x² = 100 $$\times$$​ 20 = 2000

Simple interest = $$\frac{2000 \times 10 \times 3}{100} = 600$$​​