Calculate the amount and the compound interest on ₹ 64,000 for 3 years at $7\dfrac{1}{2}$% per annum, compounded annually.

Given,

P = ₹ 64,000

n = 3 years

r = $7\dfrac{1}{2}$% = 7.5%

By formula,

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

Substituting values we get :

$\Rightarrow A = 64000\Big(1 + \dfrac{7.5}{100}\Big)^3 \\[1em] \Rightarrow A = 64000\Big(\dfrac{100+7.5}{100}\Big)^3 \\[1em] \Rightarrow A = 64000\Big(\dfrac{107.5}{100}\Big)^3 \\[1em] \Rightarrow A = 64000 \times \Big(\dfrac{21.5}{20}\Big)^3 \\[1em] \Rightarrow A = 64000 \times \dfrac{9938.375}{8000} \\[1em] \Rightarrow A = ₹ 79,507.$

Compound interest = Final amount - Initial principal = ₹ 79,507 - ₹ 64,000 = ₹ 15,507

Hence, amount = ₹ 79,507 and compound interest = ₹ 15,507.