Each of A and B opened a recurring deposit account in a bank. If A deposited ₹ 1200 per month for 3 years and B deposited ₹ 1500 per month for $2\dfrac{1}{2}$ years: find, on maturity, who will get more amount and by how much ? The rate of interest paid by bank is 10% per annum.

For A,

Given, P = ₹ 1200, n = (3 × 12) = 36 months and r = 10%

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

$\therefore I = ₹ 1200 \times \dfrac{36 \times 37}{2 \times 12} \times \dfrac{10}{100} \\[1em] = ₹ 1200 \times \dfrac{3 \times 37}{20} \\[1em] = ₹ 60 \times 3 \times 37 \\[1em] = ₹ 6660.$

Sum deposited = P × n = ₹ 1200 × 36 = ₹ 43200.

Maturity value = Sum deposited + Interest = ₹ 43200 + ₹ 6660 = ₹ 49860.

For B,

Given, P = ₹ 1500, n = (2 × 12 + 6) = 30 months and r = 10%

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

$\therefore I = ₹ 1500 \times \dfrac{30 \times 31}{2 \times 12} \times \dfrac{10}{100} \\[1em] = ₹ 1500 \times \dfrac{31}{8} \\[1em] = ₹ 5812.50$

Sum deposited = P × n = ₹ 1500 × 30 = ₹ 45000.

Maturity value = Sum deposited + Interest = ₹ 45000 + ₹ 5812.50 = ₹ 50812.50.

Difference between maturity value received by A and B is = ₹ 50812.50 - ₹ 49860 = ₹ 952.50.

Hence, B will receive more amount of ₹ 952.50.