The difference between the compound interest, compounded annually and the simple interest if ₹47,100 is deposited at 9% rate of interest per annum for 2 years is:

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 2)

Answer 1

Shortcut Trick

Given:

Principal (P) = ₹47,100

Rate (R) = 9%

Time = 2 years

Formula used:

Difference for 2 years = P\(\times\bigl(\frac{R}{100}\bigr)^2\)

Calculations:

⇒ \(\frac{R}{100} = \frac{9}{100} = 0.09\)

⇒ \((0.09)^2 = 0.0081\)

⇒ Difference = 47100 × 0.0081 = 381.51

∴ The difference between CI and SI for 2 years = ₹381.51.

Alternate Method

Formula used:

Simple interest (SI) = \(\frac{P×r×t}{100}\)

Compound interest (CI) = P\(\bigl(1+\frac{r}{100}\bigr)^t - 1\)

Calculations:

SI = \(\frac{47100×9×2}{100}\) = \(47100×0.18\) = 8478

CI = 47100\(\bigl(1+\frac{9}{100}\bigr)^2 - 1\) = 47100\(×(1.09^2 -1)\)

1.09² = 1.1881 ⇒ CI = 47100\(×0.1881\) = 8859.51

Difference = CI – SI = 8859.51 – 8478 = 381.51

∴ The difference between compound and simple interest = ₹381.51.