If in 3 years at simple interest the principal increases by 18%, what will be the compound interest (in Rs.) earned on Rs.25,000 in 3 years at the same rate?

Given:

Principal (P) = ₹25,000

Time (t) = 3 years

Principal increases by 18% in 3 years at simple interest

Formula used:

Simple Interest (SI) = P × R × T / 100

Compound Interest (CI) = P × ((1 + R/100)^t - 1)

Calculations:

Let the rate of interest be R%.

For Simple Interest:

SI = 18% of 25000

SI = 25000 × 18 / 100

⇒ SI = 4500

Since SI = P × R × T / 100

4500 = 25000 × R × 3 / 100

⇒ 4500 = 75000R / 100

⇒ 4500 × 100 = 75000R

⇒ R = 450000 / 75000

⇒ R = 6%

For Compound Interest:

CI = 25000 × ((1 + 6/100)³ - 1)

⇒ CI = 25000 × ((1 + 0.06)³ - 1)

⇒ CI = 25000 × ((1.06)³ - 1)

⇒ CI = 25000 × (1.191016 - 1)

⇒ CI = 25000 × 0.191016

⇒ CI = 4775.4

∴ The correct answer is option (1).

Alternate MethodGiven that 3 years at simple interest the principal increases by 18%

Then the rate R = 6%

P = 25000, T = 3 years

For Compound Interest:

CI = 25000 × ((1 + 6/100)3 - 1)

CI = 4775.4