A certain sum amounts to ₹ 5292 in two years and ₹ 5556.60 in three years, interest being compounded annually. Find :

(i) the rate of interest

(ii) the original sum.

(i) Given,

Amount in two years = ₹ 5292

Amount in three years = ₹ 5556.60

Difference between the amounts of two successive years

= ₹ 5556.60 - ₹ 5292 = ₹ 264.60

∴ ₹ 264.60 is the interest of one year on ₹ 5292.

By formula,

Rate of interest = $\dfrac{I \times 100}{P \times T} = \dfrac{264.60 \times 100}{5292 \times 1} = \dfrac{100}{20}$ = 5%.

Hence, rate of interest = 5%.

(ii) Let original sum be ₹ x.

For 1st year :

P = ₹ x

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 5 \times 1}{100} = \dfrac{x}{20}$.

Amount = P + I = $x + \dfrac{x}{20} = \dfrac{21x}{20}$.

For second year :

P = ₹ $\dfrac{21x}{20}$

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{\dfrac{21x}{20} \times 5 \times 1}{100} = \dfrac{21x}{400}$.

Amount = P + I = $\dfrac{21x}{20} + \dfrac{21x}{400} = \dfrac{420x + 21x}{400} = \dfrac{441x}{400}$.

Given,

Amount after 2 years = ₹ 5292

$\therefore \dfrac{441x}{400} = 5292 \\[1em] \Rightarrow x = \dfrac{5292 \times 400}{441} = 4800.$

Hence, original sum = ₹ 4800.