A sum of ₹ 2,000 is put at 10% compound interest. The amount at the end of 2 years will be :

1. ₹ 400

2. ₹ 420

3. ₹ 2420

4. ₹ 4,840

For 1st year:

P = ₹ 2,000

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{2,000 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{20,000}{100}\\[1em] = ₹ 200$

And

$\text{Amount = P + Interest}\\[1em] = ₹ 2,000 + 200\\[1em] = ₹ 2,200$

For 2nd year:

P = ₹ 2,200

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{2,200 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{22,000}{100}\\[1em] = ₹ 220$

And

$\text{Final amount = P + Interest}\\[1em] = ₹ 2,200 + 220\\[1em] = ₹ 2,420$

Hence, option 3 is the correct option.