A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in `15^(t h)` year since he deposited the amount and also calculate the total amount after 20 years.

Explanation

To solve the problem step by step, we will calculate the amount after 15 years and then the amount after 20 years using the simple interest formula.

### Step 1: Identify the given values
- Principal (P) = Rs 10,000
- Rate of interest (R) = 5% per annum
- Time (t) for the first part = 15 years
- Time (t) for the second part = 20 years

### Step 2: Calculate the simple interest for 1 year
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times t}{100} \]
For 1 year (t = 1):
\[ SI = \frac{10000 \times 5 \times 1}{100} = \frac{50000}{100} = 500 \text{ Rs} \]

### Step 3: Calculate the total amount after 15 years
Since the simple interest remains constant each year, the total simple interest for 15 years is:
\[ SI_{15} = SI \times 15 = 500 \times 15 = 7500 \text{ Rs} \]
Now, the total amount (A) after 15 years is given by:
\[ A = P + SI_{15} = 10000 + 7500 = 17500 \text{ Rs} \]

### Step 4: Calculate the total amount after 20 years
Similarly, the total simple interest for 20 years is:
\[ SI_{20} = SI \times 20 = 500 \times 20 = 10000 \text{ Rs} \]
Now, the total amount (A) after 20 years is given by:
\[ A = P + SI_{20} = 10000 + 10000 = 20000 \text{ Rs} \]

### Final Answers
- Amount after 15 years = Rs 17,500
- Amount after 20 years = Rs 20,000