Each of A and B opened a recurring deposit account in a bank. If A deposited ` ₹ 1,200` per month for `3` years and B deposited `₹ 1,500` per month for `2(1)/(2)` years, find, on maturity, who will get more amount and by how much ? The rate of interest paid by the bank is `10%` per annum.

Answer

To solve the problem step-by-step, we need to calculate the maturity amounts for both A and B based on their respective deposits and the interest rate provided.

### Step 1: Calculate the maturity amount for A

1. **Monthly Deposit (A)**: ₹1,200
2. **Duration (A)**: 3 years = 3 × 12 = 36 months
3. **Rate of Interest**: 10% per annum

#### Principal Amount for A:
- Principal Amount = Monthly Deposit × Number of Months
- Principal Amount = ₹1,200 × 36 = ₹43,200

#### Interest Calculation for A:
- Interest Formula:
\[ \text{Interest} = \frac{\text{Principal for one month} \times n \times (n + 1)}{24} \times \text{Rate of Interest} \]
- Here, Principal for one month = ₹1,200, n = 36 months
- Interest =
\[ \frac{1,200 \times 36 \times 37}{24} \times \frac{10}{100} \]
- Simplifying:
\[ = \frac{1,200 \times 36 \times 37}{240} \]
\[ = \frac{1,200 \times 1,332}{240} = \frac{1,598,400}{240} = ₹6,660 \]

#### Maturity Amount for A:
- Maturity Amount = Principal Amount + Interest
- Maturity Amount = ₹43,200 + ₹6,660 = ₹49,860

### Step 2: Calculate the maturity amount for B

1. **Monthly Deposit (B)**: ₹1,500
2. **Duration (B)**: 2.5 years = 2.5 × 12 = 30 months
3. **Rate of Interest**: 10% per annum

#### Principal Amount for B:
- Principal Amount = Monthly Deposit × Number of Months
- Principal Amount = ₹1,500 × 30 = ₹45,000

#### Interest Calculation for B:
- Interest Formula:
\[ \text{Interest} = \frac{\text{Principal for one month} \times n \times (n + 1)}{24} \times \text{Rate of Interest} \]
- Here, Principal for one month = ₹1,500, n = 30 months
- Interest =
\[ \frac{1,500 \times 30 \times 31}{24} \times \frac{10}{100} \]
- Simplifying:
\[ = \frac{1,500 \times 30 \times 31}{240} \]
\[ = \frac{1,500 \times 930}{240} = \frac{1,395,000}{240} = ₹5,812.5 \]

#### Maturity Amount for B:
- Maturity Amount = Principal Amount + Interest
- Maturity Amount = ₹45,000 + ₹5,812.5 = ₹50,812.5

### Step 3: Compare the maturity amounts of A and B

- Maturity Amount of A = ₹49,860
- Maturity Amount of B = ₹50,812.5

### Step 4: Determine who gets more and by how much

- Difference = Maturity Amount of B - Maturity Amount of A
- Difference = ₹50,812.5 - ₹49,860 = ₹952.5

### Conclusion:
B will receive more amount than A. The amount by which B exceeds A is ₹952.5.

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