#### 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 ½ years.

**Solution:**

First case-

Principal = ₹ 20000

Rate = 10% p.a.

Period = 2 ½ = 5/2 years

We know that

Simple interest = Prt/100

Substituting the values

= (20000 × 10 × 5)/ (100 × 2)

= ₹ 5000

Second case-

Principal = ₹ 20000

Rate = 10% p.a.

Period = 2 ½ years at compound interest

We know that

Amount = P (1 + r/100)^{n}

Substituting the values

= 20000 (1 + 10/100)^{2} (1 + 10/ (2 × 100))^{2}

By further calculation

= 20000 × 11/10 × 11/10 × 21/20

= ₹ 25410

Here

Compound Interest = A – P

Substituting the values

= 25410 – 20000

= ₹ 5410

So his gain after 2 years = CI – SI

We get

= 5410 – 5000

= ₹ 410

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