What principal will amount to ₹ 9856 in two years, if the rates of interest for successive years are 10% and 12% respectively?

Given,

A = ₹ 9856

r₁ = 10%

r₂ = 12%

n = 2 years

Let principal amount be ₹ x.

By formula,

A = $P\Big(1 + \dfrac{r$1}{100}\Big)\Big(1 + \dfrac{r2}{100}\Big)

Substituting values we get :

$\Rightarrow 9856 = x\Big(1 + \dfrac{10}{100}\Big)\Big(1 + \dfrac{12}{100}\Big) \\[1em] \Rightarrow 9856 = x \times \dfrac{110}{100} \times \dfrac{112}{100} \\[1em] \Rightarrow 9856 = x \times \dfrac{11}{10} \times \dfrac{28}{25} \\[1em] \Rightarrow x = \dfrac{9856 \times 10 \times 25}{11 \times 28} \\[1em] \Rightarrow x = \dfrac{2464000}{308} = ₹8000.$

Hence, principal amount = ₹ 8000.