Mr. Sharma lends ₹ 24,000 at 13% p.a. simple interest and an equal sum at 12% p.a. compound interest. Find the total interest earned by Mr. Sharma in 2 years.

For simple interest

P = ₹ 24,000

R = 13%

T = 2 years

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{24,000 \times 13 \times 2}{100}\Big)\\[1em] = \Big(\dfrac{6,24,000}{100}\Big)\\[1em] = ₹ 6,240$

For compound interest

P = ₹ 24,000

R = 12%

n = 2 years

$\text{A} = P\Big[1 + \dfrac{R}{100}\Big]^n\\[1em] = 24,000\Big[1 + \dfrac{12}{100}\Big]^2\\[1em] = 24,000\Big[1 + \dfrac{3}{25}\Big]^2\\[1em] = 24,000\Big[\dfrac{25}{25} + \dfrac{3}{25}\Big]^2\\[1em] = 24,000\Big[\dfrac{(25 + 3)}{25}\Big]^2\\[1em] = 24,000\Big[\dfrac{28}{25}\Big]^2\\[1em] = 24,000\Big[\dfrac{784}{625}\Big]\\[1em] = \Big[\dfrac{1,88,16,000}{625}\Big]\\[1em] = ₹ 30,105.60$

And

$\text{C.I. = A - P}\\[1em] = ₹ (30,105.6 - 24,000)\\[1em] = ₹ 6,105.60$

Total interest = ₹ 6,240 + ₹ 6,105.60 = ₹ 12,345.60

Hence, total interest earned by Mr. Sharma in 2 years = ₹ 12,345.60