Anu invests Rs. 5000 in a bond on which interest is given at 4% per annum during the first year, 5% during the second year and 10% during the third year. How much does she get at the end of the third year.

Answer

To solve the problem step by step, we will calculate the amount Anu receives at the end of the third year by applying the compound interest formula for different rates of interest for each year.

### Step 1: Understand the problem
Anu invests Rs. 5000 with different interest rates for three years:
- Year 1: 4%
- Year 2: 5%
- Year 3: 10%

### Step 2: Identify the formula
The formula for calculating the amount \( A \) after \( n \) years with different rates of interest is:
\[ A = P \times (1 + \frac{R_1}{100}) \times (1 + \frac{R_2}{100}) \times (1 + \frac{R_3}{100}) \]
Where:
- \( P \) = Principal amount (initial investment)
- \( R_1, R_2, R_3 \) = Interest rates for each year

### Step 3: Substitute the values
Here, \( P = 5000 \), \( R_1 = 4 \), \( R_2 = 5 \), and \( R_3 = 10 \).
Substituting these values into the formula gives:
\[ A = 5000 \times (1 + \frac{4}{100}) \times (1 + \frac{5}{100}) \times (1 + \frac{10}{100}) \]

### Step 4: Calculate each term
1. Calculate \( 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \)
2. Calculate \( 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \)
3. Calculate \( 1 + \frac{10}{100} = 1 + 0.10 = 1.10 \)

### Step 5: Substitute back into the formula
Now substitute these values back into the equation:
\[ A = 5000 \times 1.04 \times 1.05 \times 1.10 \]

### Step 6: Perform the multiplication
1. First, calculate \( 1.04 \times 1.05 \):
\[ 1.04 \times 1.05 = 1.092 \]
2. Next, multiply this result by \( 1.10 \):
\[ 1.092 \times 1.10 = 1.2012 \]
3. Finally, multiply by the principal:
\[ A = 5000 \times 1.2012 = 6006 \]

### Step 7: Conclusion
At the end of the third year, Anu will receive Rs. 6006.