Find the amount and the compound interest on ₹ 7,500 for 2 years 8 months at 10% p.a., compounded annually.

Given,

P = ₹ 7,500

n = 2 years 8 months

= 2 $\dfrac{8}{12}$ years = 2 $\dfrac{2}{3}$ years

r = 10%

By formula,

$A = P\Big(1 + \dfrac{r}{100}\Big)^n \Big(1 + \dfrac{\dfrac{2}{3}r}{100}\Big)$

Substituting values we get :

$\Rightarrow A = 7500\Big(1 + \dfrac{10}{100}\Big)^2 \Big(1 + \dfrac{\dfrac{2}{3} \times 10}{100}\Big) \\[1em] \Rightarrow A = 7500\Big(\dfrac{100+10}{100}\Big)^2 \Big(1 + \dfrac{20}{300}\Big) \\[1em] \Rightarrow A = 7500\Big(\dfrac{110}{100}\Big)^2 \Big(\dfrac{300 + 20}{300}\Big) \\[1em] \Rightarrow A = 7500\Big(\dfrac{11}{10}\Big)^2 \Big(\dfrac{320}{300}\Big)\\[1em] \Rightarrow A = 7500 \times \dfrac{121}{100} \times \dfrac{32}{30}\\[1em] \Rightarrow A = ₹ 9,680$

C.I. = A - P = ₹ 9,680 - ₹ 7,500 = ₹ 2,180

Hence, amount = ₹ 9,680 and compound interest = ₹ 2,180.