There is a 60% increase in an amount in 5 years at simple interest. What will be the compound interest on 6250 for two years at the same rate of interest, when the interest is compounded yearly?

Options

A. Rs 1, 500
B. Rs 1,590
C. Rs 1, 560
D. Rs 1, 480

Answer

To solve the problem step by step, we need to find the compound interest on Rs. 6250 for 2 years at the same rate of interest that leads to a 60% increase in an amount in 5 years at simple interest.

### Step 1: Determine the Simple Interest Rate
Given that there is a 60% increase in an amount in 5 years at simple interest, we can express this as:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- SI = Simple Interest
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

Since the increase is 60%, we can write:
\[ \text{SI} = 0.6P \]

Substituting this into the formula:
\[ 0.6P = \frac{P \times R \times 5}{100} \]

### Step 2: Simplify to Find the Rate
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 0.6 = \frac{R \times 5}{100} \]

Now, solving for \( R \):
\[ R = \frac{0.6 \times 100}{5} = 12\% \]

### Step 3: Calculate the Compound Interest
Now that we know the rate of interest is 12%, we can calculate the compound interest on Rs. 6250 for 2 years.

The formula for compound interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Substituting the known values:
- P = 6250
- R = 12
- T = 2

### Step 4: Substitute Values into the Formula
\[ CI = 6250 \left(1 + \frac{12}{100}\right)^2 - 6250 \]
\[ CI = 6250 \left(1 + 0.12\right)^2 - 6250 \]
\[ CI = 6250 \left(1.12\right)^2 - 6250 \]

### Step 5: Calculate \( (1.12)^2 \)
Calculating \( (1.12)^2 \):
\[ (1.12)^2 = 1.2544 \]

### Step 6: Substitute Back to Find CI
Now substitute back:
\[ CI = 6250 \times 1.2544 - 6250 \]
\[ CI = 7835 - 6250 \]
\[ CI = 1585 \]

### Step 7: Final Calculation
Thus, the compound interest is:
\[ CI = 1585 \]

### Conclusion
The compound interest on Rs. 6250 for 2 years at the same rate of interest is Rs. 1585.