If the interest of a certain sum for the first year at `8%` p.a. compound interest is Rs. 48. What will be the interest for the second year ?

Options

A. Rs.52.55
B. Rs.51.84
C. Rs.58.60
D. Rs.53.04

Answer

To solve the problem step by step, we need to find the interest for the second year given that the interest for the first year at 8% p.a. compound interest is Rs. 48.

### Step 1: Understand the relationship between the first and second year interest in compound interest.
In compound interest, the interest for the first year is calculated on the principal amount. For the second year, the interest is calculated on the new principal, which is the original principal plus the interest earned in the first year.

### Step 2: Calculate the principal amount.
Since the interest for the first year is Rs. 48 at 8%, we can find the principal amount (P) using the formula for interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- Interest = Rs. 48
- R = 8%
- T = 1 year

Rearranging the formula to find P:
\[ P = \frac{\text{Interest} \times 100}{R \times T} \]
Substituting the values:
\[ P = \frac{48 \times 100}{8 \times 1} = \frac{4800}{8} = 600 \]

### Step 3: Calculate the interest for the second year.
Now that we have the principal amount, we can calculate the interest for the second year. The interest for the second year will be calculated on the new principal, which is the original principal plus the interest from the first year:
\[ \text{New Principal} = P + \text{Interest from first year} = 600 + 48 = 648 \]
Now, we calculate the interest for the second year:
\[ \text{Interest for second year} = \frac{648 \times 8}{100} = 51.84 \]

### Step 4: Conclusion
The interest for the second year is Rs. 51.84.

### Final Answer:
The interest for the second year is Rs. 51.84.

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