Vikram borrowed ₹20000 from a bank at 10% per annum simple interest. He lent it to his friend Venkat at the same rate but compounded annually. Find his gain after $2\dfrac{1}{2}$ years.

Simple interest = $\dfrac{P \times R \times T}{100}.$

∴ S.I. = $\dfrac{20000 \times 10 \times 2.5}{100} = \dfrac{500000}{100}$ = ₹5000.

Calculating, compound interest :

Principal for first year = ₹20000.

Interest for first year = $\dfrac{20000 \times 10 \times 1}{100} = \dfrac{200000}{100}$ = ₹2000.

Amount after first year = ₹20000 + ₹2000 = ₹22000.

Principal for second year = ₹22000.

Interest for second year = $\dfrac{22000 \times 10 \times 1}{100} = \dfrac{220000}{100}$ = ₹2200.

Amount after second year = ₹22000 + ₹2200 = ₹24200.

Principal for next $\dfrac{1}{2}$ year = ₹24200.

Interest for next $\dfrac{1}{2}$ year = $\dfrac{24200 \times 10 \times \dfrac{1}{2}}{100} = \dfrac{242000}{200}$ = ₹1210.

Amount after $2\dfrac{1}{2}$ year = ₹24200 + ₹1210 = ₹25410.

Compound interest = Final amount - principal = ₹25410 - ₹20000 = ₹5410.

Difference between C.I. and S.I. = ₹5410 - ₹5000 = ₹410.

Hence, Venkat gained ₹410 after $2\dfrac{1}{2}$ years.