Find the compound interest correct to the nearest rupee, on ₹ 2400 for $2\dfrac{1}{2}$ years at 5 percent per annum.

For first year :

P = ₹ 2400

T = 1 year

R = 5%

I = $\dfrac{P \times R \times T}{100} = \dfrac{2400 \times 1 \times 5}{100}$ = ₹ 120.

Amount = P + I = ₹ 2400 + ₹ 120 = ₹ 2520.

For second year :

P = ₹ 2520

T = 1 year

R = 5%

I = $\dfrac{P \times R \times T}{100} = \dfrac{2520 \times 1 \times 5}{100}$ = ₹ 126.

Amount = P + I = ₹ 2520 + ₹ 126 = ₹ 2646.

For next half-year :

P = ₹ 2646

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

R = 5%

I = $\dfrac{P \times R \times T}{100} = \dfrac{2646 \times \dfrac{1}{2} \times 5}{100}$ = ₹ 66.15

Amount = P + I = ₹ 2646 + ₹ 66.15 = ₹ 2712.15

Compound interest = Final amount - Initial principal

= ₹ 2712.15 - ₹ 2400 = ₹ 312.15 ≈ ₹ 312.

Hence, compound interest = ₹ 312.