To solve the problem step by step, we will calculate the maturity value of both recurring deposit accounts and then compare them.
### Step 1: Calculate the maturity value of the first recurring deposit (RD1)
Mohit deposits ₹800 per month for 6 years.
1. **Total number of months (n)** = 6 years × 12 months/year = 72 months.
2. **Principal (P)** = ₹800 × 72 months = ₹57,600.
3. **Simple Interest (SI)** = P × n × (n + 1) / 2 × (Rate/100) × (1/12)
- Here, n = 72, Rate = 10% per annum.
- SI = ₹800 × 72 × (72 + 1) / 2 × (10/100) × (1/12)
- SI = ₹800 × 72 × 73 / 2 × 0.1 / 12
- SI = ₹800 × 72 × 73 / 240
- SI = ₹800 × 21.5 = ₹17,200.
4. **Total maturity value (M1)** = Principal + SI = ₹57,600 + ₹17,200 = ₹74,800.
### Step 2: Calculate the maturity value of the second recurring deposit (RD2)
Mohit starts this deposit after 2 years, so he deposits ₹1,500 per month for the remaining 4 years.
1. **Total number of months (n)** = 4 years × 12 months/year = 48 months.
2. **Principal (P)** = ₹1,500 × 48 months = ₹72,000.
3. **Simple Interest (SI)** = P × n × (n + 1) / 2 × (Rate/100) × (1/12)
- Here, n = 48, Rate = 10% per annum.
- SI = ₹1,500 × 48 × (48 + 1) / 2 × (10/100) × (1/12)
- SI = ₹1,500 × 48 × 49 / 2 × 0.1 / 12
- SI = ₹1,500 × 48 × 49 / 240
- SI = ₹1,500 × 9.8 = ₹14,700.
4. **Total maturity value (M2)** = Principal + SI = ₹72,000 + ₹14,700 = ₹86,700.
### Step 3: Compare the maturity values of both RDs
1. **Maturity value of RD1** = ₹74,800.
2. **Maturity value of RD2** = ₹86,700.
### Step 4: Find out which RD gives more money and by how much
1. **Difference** = M2 - M1 = ₹86,700 - ₹74,800 = ₹11,900.
### Final Answer
At the end of 6 years, the second RD will give more money by ₹11,900.
---
