A man saves `Rs. 2000` at the end of each year and invests the money at `5%` compound interest. At the end of 3 years he will have :

Options

A. `Rs. 4305`
B. `Rs. 6305`
C. `Rs. 4205`
D. `Rs. 2205`

Answer

To solve the problem step by step, we will calculate the total amount a man will have after saving Rs. 2000 at the end of each year and investing it at a compound interest rate of 5% for 3 years.

### Step 1: Understand the Savings and Interest
The man saves Rs. 2000 at the end of each year. This means:
- At the end of Year 1, he saves Rs. 2000.
- At the end of Year 2, he saves another Rs. 2000.
- At the end of Year 3, he saves yet another Rs. 2000.

### Step 2: Calculate the Amount for Each Year
1. **End of Year 1:**
- Amount saved = Rs. 2000
- Interest for Year 1 = 5% of Rs. 2000 = \( \frac{5}{100} \times 2000 = Rs. 100 \)
- Total amount at the end of Year 1 = Rs. 2000 + Rs. 100 = Rs. 2100

2. **End of Year 2:**
- Amount saved = Rs. 2000
- Total amount carried forward from Year 1 = Rs. 2100
- Total amount before adding Year 2 savings = Rs. 2100 + Rs. 2000 = Rs. 4100
- Interest for Year 2 = 5% of Rs. 4100 = \( \frac{5}{100} \times 4100 = Rs. 205 \)
- Total amount at the end of Year 2 = Rs. 4100 + Rs. 205 = Rs. 4305

3. **End of Year 3:**
- Amount saved = Rs. 2000
- Total amount carried forward from Year 2 = Rs. 4305
- Total amount before adding Year 3 savings = Rs. 4305 + Rs. 2000 = Rs. 6305
- Interest for Year 3 = 5% of Rs. 6305 = \( \frac{5}{100} \times 6305 = Rs. 315.25 \)
- Total amount at the end of Year 3 = Rs. 6305 + Rs. 315.25 = Rs. 6620.25

### Final Amount
At the end of 3 years, the total amount he will have is **Rs. 6620.25**.

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