Find the compound interest for third year on Rs 20000 at the rate of 7%?

Options

A. ₹ 2529.04
B. ₹ 2404.29
C. ₹ 2429.04
D. ₹ 2504.29

Answer

To find the compound interest for the third year on Rs 20,000 at the rate of 7%, we can follow these steps:

### Step 1: Understand the Concept of Compound Interest
Compound interest is calculated on the initial principal, which also includes all of the accumulated interest from previous periods. To find the compound interest for the third year, we need to determine the amount at the end of the second year first.

### Step 2: Calculate the Amount at the End of the Second Year
To find the amount at the end of the second year, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after \( n \) years
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

For our case:
- \( P = 20000 \)
- \( r = 7\% \)
- \( n = 2 \)

Substituting the values:
\[ A = 20000 \left(1 + \frac{7}{100}\right)^2 \]
\[ A = 20000 \left(1 + 0.07\right)^2 \]
\[ A = 20000 \left(1.07\right)^2 \]
\[ A = 20000 \times 1.1449 \]
\[ A \approx 22898 \]

### Step 3: Calculate the Compound Interest for the Third Year
Now that we have the amount at the end of the second year, we can calculate the compound interest for the third year. The compound interest for the third year is the interest earned on the amount at the end of the second year.

The interest for the third year can be calculated as:
\[ \text{Compound Interest for 3rd Year} = A \times \frac{r}{100} \]
Where \( A \) is the amount at the end of the second year.

Substituting the values:
\[ \text{Compound Interest for 3rd Year} = 22898 \times \frac{7}{100} \]
\[ \text{Compound Interest for 3rd Year} = 22898 \times 0.07 \]
\[ \text{Compound Interest for 3rd Year} \approx 1602.86 \]

### Final Answer
The compound interest for the third year on Rs 20,000 at the rate of 7% is approximately Rs 1602.86.

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