A certain sum of money amounts to ₹ 4,500 in first year; to ₹ 5,175 in second year and to ₹ 6,210 in third year.Find the rate of interest for the (i) second year (ii) third year.

(i) Given: Amount at the end of the first year = ₹ 4,500

Amount at the end of the second year = ₹ 5,175

Amount at the end of the third year = ₹ 6,210

Interest for second year = ₹ 5,175 - ₹ 4,500 = ₹ 675

For the second year:

P = ₹ 4,500, R = R %, T = 1 year, I = ₹ 675

$\text{Interest} = \dfrac{P \times R \times T}{100}\\[1em] \Rightarrow 675 = \dfrac{4,500 \times R \times 1}{100}\\[1em] \Rightarrow R = \dfrac{675 \times 100}{4,500}\\[1em] \Rightarrow R = 15$

Hence, the rate of interest for second year = 15%.

(ii) Interest for third year = ₹ 6,210 - ₹ 5,175 = ₹ 1,035

For the third year:

P = ₹ 5,175, R = R %, T = 1 year, I = ₹ 1,035

$\text{Interest} = \dfrac{P \times R \times T}{100}\\[1em] \Rightarrow 1,035 = \dfrac{5,175 \times R \times 1}{100}\\[1em] \Rightarrow R = \dfrac{1,035 \times 100}{5,175}\\[1em] \Rightarrow R = 20$

Hence, the rate of interest for third year = 20%.