What sum will amount to Rs. 15916.59 in 3 years at compound interest, the interest for first, second and third year being 3, 2 and 1 percent respectively?

Answer

To solve the problem of finding the principal amount that will amount to Rs. 15,916.59 in 3 years at compound interest with varying rates for each year, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Rates of Interest**:
- For the first year (R1): 3%
- For the second year (R2): 2%
- For the third year (R3): 1%

2. **Write the Formula for Compound Interest**:
The formula for the amount (A) in terms of the principal (P) and the rates of interest for each year is:
\[ A = P \times \left(1 + \frac{R1}{100}\right) \times \left(1 + \frac{R2}{100}\right) \times \left(1 + \frac{R3}{100}\right) \]

3. **Substitute the Values**:
Given that the amount (A) is Rs. 15,916.59, we can substitute the values into the formula:
\[ 15916.59 = P \times \left(1 + \frac{3}{100}\right) \times \left(1 + \frac{2}{100}\right) \times \left(1 + \frac{1}{100}\right) \]
This simplifies to:
\[ 15916.59 = P \times \left(1.03\right) \times \left(1.02\right) \times \left(1.01\right) \]

4. **Calculate the Product of the Factors**:
Now, calculate the product of the factors:
\[ 1.03 \times 1.02 \times 1.01 = 1.060606 \]

5. **Rearranging the Equation**:
Rearranging the equation to solve for P:
\[ P = \frac{15916.59}{1.060606} \]

6. **Perform the Division**:
Now, perform the division:
\[ P \approx \frac{15916.59}{1.060606} \approx 15000 \]

7. **Conclusion**:
Therefore, the principal amount that will amount to Rs. 15,916.59 in 3 years at the given compound interest rates is Rs. 15,000.

### Final Answer:
The principal amount is Rs. 15,000.

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