Neeraj saves Rs. 400 at the end of each year and lends this saving at `5%` p.a. compound interest.How much will it worth at the end of 3 years ?

Options

A. Rs.1312.50
B. Rs.1284
C. Rs.1315
D. Rs.1324.05

Answer

To find out how much Neeraj's savings will be worth at the end of 3 years when he saves Rs. 400 at the end of each year and lends it at 5% per annum compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables:**
- Annual Savings (P) = Rs. 400
- Rate of Interest (R) = 5% per annum
- Time (T) = 3 years

2. **Calculate the Amount for Each Year:**
Since Neeraj saves Rs. 400 at the end of each year, we need to calculate the compound interest for each of these savings separately, as they will each accrue interest for a different number of years.

- **For the first Rs. 400 (saved at the end of Year 1):**
- This amount will earn interest for 3 years.
- Amount (A1) = P(1 + R/100)^T = 400(1 + 5/100)^3
- A1 = 400(1.05)^3 = 400 * 1.157625 = Rs. 463.05

- **For the second Rs. 400 (saved at the end of Year 2):**
- This amount will earn interest for 2 years.
- Amount (A2) = P(1 + R/100)^T = 400(1 + 5/100)^2
- A2 = 400(1.05)^2 = 400 * 1.1025 = Rs. 441.00

- **For the third Rs. 400 (saved at the end of Year 3):**
- This amount will earn interest for 1 year.
- Amount (A3) = P(1 + R/100)^T = 400(1 + 5/100)^1
- A3 = 400(1.05)^1 = 400 * 1.05 = Rs. 420.00

3. **Total Amount at the End of 3 Years:**
- Total Amount (A) = A1 + A2 + A3
- A = 463.05 + 441.00 + 420.00
- A = Rs. 1324.05

### Final Answer:
At the end of 3 years, Neeraj's savings will be worth approximately **Rs. 1324.05**.