The simple interest accrued on a sum of certain principal in 8 yr at the rate of 13% per year is ₹6500. What would be the compound interest accrued on that principal at the rate of 8% per year in 2yr?

Options

A. ₹1,040
B. ₹1,020
C. ₹1,060
D. ₹1,200

Explanation

To solve the problem step by step, we will first determine the principal amount using the simple interest formula, and then we will calculate the compound interest based on that principal.

### Step 1: Calculate the Principal Amount

We know that the formula for Simple Interest (SI) is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per year
- \(T\) = Time in years

From the question:
- \(SI = 6500\)
- \(R = 13\%\)
- \(T = 8\) years

We need to find \(P\). Rearranging the formula to solve for \(P\):

\[ P = \frac{SI \times 100}{R \times T} \]

Substituting the known values:

\[ P = \frac{6500 \times 100}{13 \times 8} \]

Calculating the denominator:

\[ 13 \times 8 = 104 \]

Now substituting back into the equation:

\[ P = \frac{650000}{104} \]

Calculating \(P\):

\[ P = 6250 \]

### Step 2: Calculate the Compound Interest

Now that we have the principal amount, we can calculate the compound interest (CI) for 2 years at an 8% interest rate. The formula for Compound Interest is:

\[ CI = P \left(1 + \frac{R}{100}\right)^n - P \]

Where:
- \(n\) = number of years

Substituting the values we have:

\[ CI = 6250 \left(1 + \frac{8}{100}\right)^2 - 6250 \]

Calculating \(1 + \frac{8}{100}\):

\[ 1 + \frac{8}{100} = 1.08 \]

Now substituting this into the CI formula:

\[ CI = 6250 \times (1.08)^2 - 6250 \]

Calculating \((1.08)^2\):

\[ (1.08)^2 = 1.1664 \]

Now substituting back:

\[ CI = 6250 \times 1.1664 - 6250 \]

Calculating \(6250 \times 1.1664\):

\[ 6250 \times 1.1664 = 7290 \]

Now subtracting the principal:

\[ CI = 7290 - 6250 = 1040 \]

### Final Answer

The compound interest accrued on the principal at the rate of 8% per year in 2 years is ₹1040.

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