The compound interest on ₹ 5000 at 10% per annum and in one year compounded half-yearly is :

1. ₹ 1050

2. ₹ 525

3. ₹ 512.50

4. ₹ 5512.50

Since, time is 1 year so interest will be compounded half-yearly twice.

For first half-year :

P = ₹ 5000

T = $\dfrac{1}{2}$ year

R = 10%

By formula,

Interest = $\dfrac{P \times R \times T}{100}$

Substituting values we get :

Interest = $\dfrac{5000 \times \dfrac{1}{2} \times 10}{100}$ = ₹ 250.

For second half-year :

P = ₹ 5000 + ₹ 250 = ₹ 5250

T = $\dfrac{1}{2}$ year

R = 10%

By formula,

Interest = $\dfrac{P \times R \times T}{100}$

Substituting values we get :

Interest = $\dfrac{5250 \times \dfrac{1}{2} \times 10}{100}$ = ₹ 262.50

Total compound interest = ₹ 250 + ₹ 262.50 = ₹ 512.50

Hence, Option 3 is the correct option.