What sum will amount to रु 6,593.40 in 2 years at C.I., if the rates are 10 percent and 11 percent for the two successive years ?

Explanation

To find the principal sum that will amount to रु 6,593.40 in 2 years at compound interest with rates of 10% and 11% for the two successive years, we can follow these steps:

### Step 1: Understand the Compound Interest Formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \]
where:
- \( A \) is the amount after time \( t \),
- \( P \) is the principal amount (the sum we want to find),
- \( r_1 \) is the interest rate for the first year,
- \( r_2 \) is the interest rate for the second year.

### Step 2: Substitute the Known Values
In this case:
- \( A = 6593.40 \)
- \( r_1 = 10\% \)
- \( r_2 = 11\% \)

Substituting these values into the formula gives:
\[ 6593.40 = P \left(1 + \frac{10}{100}\right) \left(1 + \frac{11}{100}\right) \]

### Step 3: Simplify the Equation
Calculating the terms inside the parentheses:
\[ 1 + \frac{10}{100} = 1 + 0.10 = 1.10 \]
\[ 1 + \frac{11}{100} = 1 + 0.11 = 1.11 \]

Now, substituting these back into the equation:
\[ 6593.40 = P \times 1.10 \times 1.11 \]

### Step 4: Calculate the Product of the Factors
Calculating the product of 1.10 and 1.11:
\[ 1.10 \times 1.11 = 1.221 \]

So the equation now looks like:
\[ 6593.40 = P \times 1.221 \]

### Step 5: Solve for \( P \)
To find \( P \), we can rearrange the equation:
\[ P = \frac{6593.40}{1.221} \]

Now, calculating the value:
\[ P = 5400 \]

### Conclusion
The principal sum that will amount to रु 6,593.40 in 2 years at compound interest is रु 5,400.

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