Find the amount and the compound interest on Rs. 12,000 in 3 years, when the rates of interest for successive years are 10%, 12% and 15% respectively.

Answer

To find the amount and the compound interest on Rs. 12,000 over 3 years with varying interest rates, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 12,000
- Time (T) = 3 years
- Rates of interest:
- First year (r1) = 10%
- Second year (r2) = 12%
- Third year (r3) = 15%

### Step 2: Use the compound interest formula
The formula for calculating the amount (A) with compound interest for different rates is:
\[ A = P \left(1 + \frac{r1}{100}\right) \left(1 + \frac{r2}{100}\right) \left(1 + \frac{r3}{100}\right) \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 12000 \left(1 + \frac{10}{100}\right) \left(1 + \frac{12}{100}\right) \left(1 + \frac{15}{100}\right) \]
This simplifies to:
\[ A = 12000 \left(1.10\right) \left(1.12\right) \left(1.15\right) \]

### Step 4: Calculate the amount step by step
1. Calculate \( 1.10 \times 1.12 \):
\[ 1.10 \times 1.12 = 1.232 \]
2. Now multiply this result by \( 1.15 \):
\[ 1.232 \times 1.15 = 1.4168 \]
3. Finally, multiply by the principal:
\[ A = 12000 \times 1.4168 = 17001.60 \]

### Step 5: Calculate the compound interest
The compound interest (CI) can be calculated using the formula:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 17001.60 - 12000 = 5001.60 \]

### Final Results
- Amount (A) = Rs. 17,001.60
- Compound Interest (CI) = Rs. 5,001.60