Find the amount and the compound interest on ₹2000 at 10% p.a. for $2\dfrac{1}{2}$ years, compounded annually.

Principal for first year = ₹2000.

Interest for the first year = ₹ $\dfrac{2000 \times 10 \times 1}{100}$ = ₹200.

Amount after one year = ₹2000 + ₹200 = ₹2200.

Principal for the second year = ₹2200.

Interest for the second year = ₹ $\dfrac{2200 \times 10 \times 1}{100}$ = ₹220

Amount after 2 years = ₹2200 + ₹220 = ₹2420.

Principal for next $\dfrac{1}{2}$ year = ₹2420.

Interest for the next $\dfrac{1}{2}$ year = ₹ $\dfrac{2420 \times 10 \times \dfrac{1}{2}}{100} = \dfrac{12100}{100}$ = ₹121.

Amount after $2\dfrac{1}{2}$ years = ₹2420 + ₹121 = ₹2541.

Compound interest for $2\dfrac{1}{2}$ years = Final amount - Principal = ₹2541 - ₹2000 = ₹541.

Hence, the amount and compound interest on ₹2000 at 10% per annum after $2\dfrac{1}{2}$ years is ₹2541 and ₹541 respectively.