If compound interest on some amount for one year is 680 and rate of interest is 5% then find the interest for second year?

Options

A. ₹680
B. ₹ 714
C. ₹ 720
D. ₹ 704

Answer

To solve the problem step-by-step, we need to calculate the compound interest for the second year based on the information given.

### Step 1: Understand the given information
We know that:
- The compound interest for the first year is Rs. 680.
- The rate of interest is 5%.

### Step 2: Calculate the principal amount
Since we know the compound interest for the first year, we can use the formula for compound interest for the first year:
\[ \text{CI} = P \times \frac{R}{100} \]
Where:
- CI = Compound Interest for the first year (Rs. 680)
- P = Principal amount
- R = Rate of interest (5%)

Rearranging the formula to find P:
\[ P = \frac{\text{CI} \times 100}{R} \]
Substituting the values:
\[ P = \frac{680 \times 100}{5} = \frac{68000}{5} = 13600 \]
So, the principal amount \( P = Rs. 13600 \).

### Step 3: Calculate the interest for the second year
The interest for the second year is calculated on the total amount after the first year, which includes the principal and the interest from the first year.

The total amount after the first year (A) can be calculated as:
\[ A = P + \text{CI} \]
Substituting the values:
\[ A = 13600 + 680 = 14280 \]

Now, we calculate the interest for the second year using the total amount:
\[ \text{Interest for second year} = A \times \frac{R}{100} \]
Substituting the values:
\[ \text{Interest for second year} = 14280 \times \frac{5}{100} = 14280 \times 0.05 = 714 \]

### Step 4: Conclusion
Thus, the interest for the second year is Rs. 714.

### Final Answer
The interest for the second year is Rs. 714.

---