Find the compound interest on Rs 20000 for 2 year and 73 days at the rate of 5%?

Options

A. ₹ 2250.70
B. ₹2230.40
C. ₹ 2270.50
D. ₹ 2240.30

Answer

To find the compound interest on Rs 20,000 for 2 years and 73 days at the rate of 5%, we will follow these steps:

### Step 1: Convert the time period into years
The total time is 2 years and 73 days. We need to convert the 73 days into years.

1 year = 365 days, so:
\[ \text{Time in years} = 2 + \frac{73}{365} \]
Calculating this gives:
\[ \text{Time in years} = 2 + 0.2 = 2.2 \text{ years} \]

### Step 2: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money).
- \( r \) = annual interest rate (in percentage).
- \( n \) = number of years the money is invested or borrowed.

Substituting the values:
- \( P = 20000 \)
- \( r = 5 \)
- \( n = 2.2 \)

### Step 3: Calculate the amount \( A \)
Substituting the values into the formula:
\[ A = 20000 \left(1 + \frac{5}{100}\right)^{2.2} \]
\[ A = 20000 \left(1 + 0.05\right)^{2.2} \]
\[ A = 20000 \left(1.05\right)^{2.2} \]

Now, calculate \( (1.05)^{2.2} \):
Using a calculator, \( (1.05)^{2.2} \approx 1.1157 \).

Now, substituting back:
\[ A \approx 20000 \times 1.1157 \approx 22314 \]

### Step 4: Calculate the compound interest
The compound interest \( CI \) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 22314 - 20000 = 2314 \]

### Step 5: Final Result
The compound interest on Rs 20,000 for 2 years and 73 days at the rate of 5% is approximately Rs 2314.