A man saves रु 3,000 every year and invests it at the end of the year at 10% compound interest. Calculate the total amount of his savings at the end of the third year.

Explanation

To calculate the total amount of savings at the end of the third year when a man saves रु 3,000 every year and invests it at the end of each year at a compound interest rate of 10%, we can follow these steps:

### Step 1: Calculate the amount at the end of the first year
- **Principal (P)** = रु 3,000
- **Rate of Interest (R)** = 10%
- **Time (T)** = 1 year

Using the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( A \) = Amount after time \( n \)
- \( r \) = Rate of interest (in decimal) = 10/100 = 0.10
- \( n \) = Number of years

For the first year:
\[ A_1 = 3000(1 + 0.10)^1 = 3000(1.10) = 3300 \]

### Step 2: Calculate the amount at the end of the second year
At the end of the second year, he saves another रु 3,000, making the total principal for the second year:
- New Principal = Previous Amount + New Savings = 3300 + 3000 = 6300

Now, calculate the amount for the second year:
\[ A_2 = 6300(1 + 0.10)^1 = 6300(1.10) = 6930 \]

### Step 3: Calculate the amount at the end of the third year
At the end of the third year, he saves another रु 3,000, making the total principal for the third year:
- New Principal = Previous Amount + New Savings = 6930 + 3000 = 9930

Now, calculate the amount for the third year:
\[ A_3 = 9930(1 + 0.10)^1 = 9930(1.10) = 10923 \]

### Final Amount
Thus, the total amount of his savings at the end of the third year is **रु 10,923**.

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