The difference between compound interest and simple interest for 3 years at the rate of 20% per annum is ₹240. What is the principal lent?

Given:

The difference between compound interest and simple interest for 3 years at the rate of 20% per annum is ₹240.

Formula Used:

Difference between Compound Interest (CI) and Simple Interest (SI) for 3 years = P × (r/100)³ + 3P × (r/100)²

Calculation:

Let the principal amount be P.

Rate (r) = 20%

Time (t) = 3 years

Difference between CI and SI for 3 years = ₹240

⇒ P × (20/100)³ + 3P × (20/100)² = 240

⇒ P × (0.2)³ + 3P × (0.2)² = 240

⇒ P × 0.008 + 3P × 0.04 = 240

⇒ 0.008P + 0.12P = 240

⇒ 0.128P = 240

⇒ P = 240 / 0.128

⇒ P = 1875

The principal lent is ₹1,875.