A certain sum, at compound interest, becomes ₹ 7,396 in 2 years and ₹ 7,950.70 in 3 years. Find the rate of interest.

Let the rate of interest be R %.

Amount for 2 years = ₹ 7,396

Amount for 3 years = ₹ 7,950.70

Interest for 3rd year = Amount for third year - Amount for second year

= ₹ 7,950.70 - ₹ 7,396

= ₹ 554.70

For the third year:

P = ₹ 7,396, R = R %, T = 1 year, I = ₹ 554.70

$\text{Interest for third year} = \dfrac{P \times R \times T}{100}\\[1em] ⇒ 554.70 = \dfrac{7,396 \times R \times 1}{100}\\[1em] ⇒ R = \dfrac{554.70 \times 100}{7,396}\\[1em] ⇒ R = \dfrac{55,470}{7,396}\\[1em] ⇒ R = 7.5$

Hence, the rate of interest = 7.5 %.