Without using formula, find the difference between the compound interest and the simple interest on ₹ 16,000 at 9% per annum in 2 years.

Compound interest:

For the first year:

P = ₹ 16,000, R = 9 %, T = 1 year

$\text{Interest} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{16,000 \times 9 \times 1}{100}\\[1em] = \dfrac{144,000}{100}\\[1em] = ₹ 1,440$

Amount at the end of first year = P + I

= ₹ 16,000 + 1,440

= ₹ 17,440

For the second year:

P = ₹ 17,440, R = 9 %, T = 1 year

$\text{Interest} = \dfrac{17,440 \times 9 \times 1}{100}\\[1em] = \dfrac{156,960}{100}\\[1em] = ₹ 1569.6$

Compound Interest of 2 years = 1,440 + 1569.6

= ₹ 3,009.6

For simple interest:

P = ₹ 16,000, R = 9 %, T = 2 year

$\text{Interest} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{16,000 \times 9 \times 2}{100}\\[1em] = \dfrac{288,000}{100}\\[1em] = ₹ 2,880$

Difference between compound interest and simple interest = ₹ 3,009.6 - ₹ 2,880 = ₹ 129.6

Hence, the difference between C.I. and S.I. = ₹ 129.6.