Salman deposits ₹1,000 every month in a recurring deposit account for 2 years. If he receives ₹26,000 on maturity, find:

(i) the total interest Salman earns.

(ii) the rate of interest.

Given,

P = ₹1,000

n = 2 years = 24 months

Maturity Value = ₹26,000

(i) The total interest Salman earns.

Sum deposited = P × n = 1,000 × 24 = ₹24,000

Maturity Value = Sum deposited + Interest

Interest = Maturity Value - Sum deposited

∴ I = ₹26,000 - ₹24,000 = ₹2,000

The total interest Salman earns is ₹2,000.

(ii) The rate of interest

I = ₹2,000

I = $P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{r}{100}$

$\therefore 2000 = 1000 \times \dfrac{24 \times 25}{24} \times \dfrac{r}{100}\\[1em] 2000 = 1000 \times 25 \times \dfrac{r}{100}\\[1em] 2000 = 250r\\[1em] r = \dfrac{2000}{250}\\[1em] r=8\%$

Hence, (i) The total interest Salman earns is ₹2,000.(ii) The rate of interest is 8% per annum.