If simple interest on sum of money for 3 years at 8% per annum is ₹ 7,500, find the compound interest on the same sum for the same period at same rate.

Given,

I = ₹ 7,500

T = 3 years

R = 8% p.a. simple interest

I = $\dfrac{P \times R \times T}{100}$

$\Rightarrow 7500 = \dfrac{P \times 8 \times 3}{100} \\[1em] \Rightarrow 7500 = \dfrac{P \times 24}{100} \\[1em] \Rightarrow P = \dfrac{7500 \times 100}{24} \\[1em] \Rightarrow P = ₹ 31,250.$

Let's calculate compound interest for this principal, rate of interest and time.

By formula,

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

$\Rightarrow A = 31250\Big(1 + \dfrac{8}{100}\Big)^3 \\[1em] \Rightarrow A = 31250\Big(\dfrac{100+8}{100}\Big)^3 \\[1em] \Rightarrow A = 31250\Big(\dfrac{108}{100}\Big)^3 \\[1em] \Rightarrow A = 31250\Big(\dfrac{27}{25}\Big)^3 \\[1em] \Rightarrow A = 31250 \times \dfrac{19683}{15625} \\[1em] \Rightarrow A = ₹ 39366.$

Compound interest = Final amount - Initial principal

= ₹ 39,366 - ₹ 31,250 = ₹ 8,116.

Hence, compound interest = ₹ 8,116.