If P = Rs. 2500, R=20% per annum, then in what time will it amount to Rs. 3600 at compound interest ?

Answer

To solve the problem step by step, we will use the formula for compound interest and the amount.

### Step 1: Understand the formula for compound amount
The formula for the amount (A) in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
where:
- \( A \) is the final amount,
- \( P \) is the principal amount,
- \( R \) is the rate of interest per annum,
- \( n \) is the time in years.

### Step 2: Substitute the known values into the formula
In this case:
- \( A = 3600 \) (the amount we want),
- \( P = 2500 \) (the principal),
- \( R = 20\% \) (the rate of interest).

Substituting these values into the formula gives:
\[ 3600 = 2500 \left(1 + \frac{20}{100}\right)^n \]

### Step 3: Simplify the equation
First, simplify \( 1 + \frac{20}{100} \):
\[ 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]

Now, the equation becomes:
\[ 3600 = 2500 (1.2)^n \]

### Step 4: Isolate \( (1.2)^n \)
To isolate \( (1.2)^n \), divide both sides by 2500:
\[ (1.2)^n = \frac{3600}{2500} \]

Calculating the right side:
\[ \frac{3600}{2500} = 1.44 \]

So we have:
\[ (1.2)^n = 1.44 \]

### Step 5: Solve for \( n \)
To find \( n \), we can take the logarithm of both sides:
\[ n \cdot \log(1.2) = \log(1.44) \]
Now, divide both sides by \( \log(1.2) \):
\[ n = \frac{\log(1.44)}{\log(1.2)} \]

### Step 6: Calculate the values
Using a calculator:
- \( \log(1.44) \approx 0.158 \)
- \( \log(1.2) \approx 0.079 \)

Now substituting these values:
\[ n \approx \frac{0.158}{0.079} \approx 2 \]

### Conclusion
Thus, the time required for the amount to grow from Rs. 2500 to Rs. 3600 at a compound interest rate of 20% per annum is approximately **2 years**.

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