Question

Both A and B opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for $2\frac{1}{2}$ years; then find who will get more amount , on maturityand by how much? The rate of interest paid by the bank is 10% per annum.

Answer 1

For A

Installment per month(P) = ₹ 1,200

Number of months(n) = 3 x 12 = 36 Months

Total Amount Deposited = 36 x 1200 = ₹ 43,200

Rate of interest(r)= 10% p.a.

$\therefore \text{Interest}=P\times \frac{n(n+1)}{2\times 12}\times \frac{r}{100}$
$=1200\times \frac{36(36+1)}{2\times 12}\times \frac{10}{100}$
$=1200\times \frac{1332}{24}\times \frac{10}{100}$ =₹ 6660

Maturity Value = Total Amount Deposited + Interest

= ₹ 43,200+ ₹ 6,660

= ₹ 49,860

For B

Installment per month(P) = ₹ 1,500

Number of months(n) = 2.5 x 12 = 30 Months

Total Amount Deposited = 1500 x 30 = ₹ 45,000

Rate of interest(r)= 10% p.a.
$\therefore \text{Interest}=P\times \frac{n(n+1)}{2\times 12}\times \frac{r}{100}$
$=1500\times \frac{30(30+1)}{2\times 12}\times \frac{10}{100}$
$=1500\times \frac{930}{24}\times \frac{10}{100}=Rs5812.5$

Maturity Value = Total Amount Deposited + Interest

= ₹ 45,000 + ₹ 5812.50

= ₹ 50,812.50

Hence, on maturity, B gets more amount than A.

Now, difference between Maturity Value of B and Maturity Value of A = ₹ 50,812.50 - ₹ 49,860
= ₹ 952.50

Thus, B gets ₹ 952.50 more than A on maturity.