A sum of Rs 25000 was give as lon on compound interest for 3 years compounded annally at 55 per annum during the first year, 6% per annum during the second year and 8% per annum during the third year. The compound interest is

Options

A. Rs 5035
B. Rs 5051
C. Rs 5072
D. Rs 5150

Answer

To solve the problem step by step, we will calculate the compound interest for a sum of Rs. 25000 over 3 years with varying interest rates for each year.

### Step 1: Understand the Formula
The formula for calculating the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \left(1 + \frac{r_3}{100}\right) \]
Where:
- \( P \) = Principal amount (initial loan)
- \( r_1 \), \( r_2 \), \( r_3 \) = Interest rates for the first, second, and third years respectively.

### Step 2: Identify the Given Values
From the problem:
- Principal \( P = 25000 \)
- Interest rates:
- \( r_1 = 5\% \) (first year)
- \( r_2 = 6\% \) (second year)
- \( r_3 = 8\% \) (third year)

### Step 3: Substitute the Values into the Formula
Now, substituting the values into the formula:
\[ A = 25000 \left(1 + \frac{5}{100}\right) \left(1 + \frac{6}{100}\right) \left(1 + \frac{8}{100}\right) \]
This simplifies to:
\[ A = 25000 \left(1 + 0.05\right) \left(1 + 0.06\right) \left(1 + 0.08\right) \]
\[ A = 25000 \times 1.05 \times 1.06 \times 1.08 \]

### Step 4: Calculate Each Component
Calculating each component:
- \( 1.05 \) (for the first year)
- \( 1.06 \) (for the second year)
- \( 1.08 \) (for the third year)

Calculating the product:
\[ A = 25000 \times 1.05 \times 1.06 \times 1.08 \]

### Step 5: Perform the Multiplication
Now, let's calculate:
1. First, calculate \( 1.05 \times 1.06 \):
\[ 1.05 \times 1.06 = 1.113 \]
2. Next, multiply by \( 1.08 \):
\[ 1.113 \times 1.08 = 1.20204 \]
3. Finally, multiply by the principal:
\[ A = 25000 \times 1.20204 = 30051 \]

### Step 6: Calculate the Compound Interest
Now, we find the compound interest (CI) using the formula:
\[ CI = A - P \]
Substituting the values:
\[ CI = 30051 - 25000 = 5051 \]

### Final Answer
Therefore, the compound interest is:
\[ \text{Compound Interest} = Rs. 5051 \]

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