A man saves rupes 5000 every years and invests it at the end of the year at 10 % P.a. Compound interest. Calculate the total amount of his savings at the end of the third years.

Answer

To solve the problem step by step, we will calculate the total amount of savings at the end of the third year, considering that the man saves Rs. 5000 at the end of each year and invests it at a compound interest rate of 10% per annum.

### Step 1: Understand the Investment
The man saves Rs. 5000 at the end of each year. He invests this amount at a compound interest rate of 10% per annum.

### Step 2: Calculate the Amount for Each Year
We will calculate the total amount for each year separately, taking into account that the amount saved in each year will earn interest for a different number of years.

#### Year 1:
- Amount saved: Rs. 5000
- Time invested: 3 years (since it will earn interest for the full 3 years)
- Amount at the end of Year 1 = Principal × (1 + Rate)^Time
- Amount = 5000 × (1 + 0.10)^3
- Amount = 5000 × (1.10)^3
- Amount = 5000 × 1.331 = Rs. 6655

#### Year 2:
- Amount saved: Rs. 5000
- Time invested: 2 years
- Amount at the end of Year 2 = 5000 × (1 + 0.10)^2
- Amount = 5000 × (1.10)^2
- Amount = 5000 × 1.21 = Rs. 6050

#### Year 3:
- Amount saved: Rs. 5000
- Time invested: 1 year
- Amount at the end of Year 3 = 5000 × (1 + 0.10)^1
- Amount = 5000 × (1.10)
- Amount = 5000 × 1.10 = Rs. 5500

### Step 3: Calculate the Total Amount at the End of the Third Year
Now, we will sum up the amounts from each year to find the total amount at the end of the third year.

Total Amount = Amount from Year 1 + Amount from Year 2 + Amount from Year 3
Total Amount = 6655 + 6050 + 5500
Total Amount = Rs. 18205

### Final Answer
The total amount of his savings at the end of the third year is Rs. 18205.

---