Romil invested Rs. 16000 for two years at compound interest and received an amount of Rs. 17640 on maturity. find the rate of interest?

Answer

To find the rate of interest for Romil's investment, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 16,000
- Amount (A) = Rs. 17,640
- Time (T) = 2 years

### Step 2: Use the formula for compound interest
The formula for the amount in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- A = Amount after time T
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 17,640 = 16,000 \left(1 + \frac{R}{100}\right)^2 \]

### Step 4: Divide both sides by the principal
To isolate the term with R, divide both sides by 16,000:
\[ \frac{17,640}{16,000} = \left(1 + \frac{R}{100}\right)^2 \]

### Step 5: Simplify the left side
Calculating the left side:
\[ \frac{17,640}{16,000} = 1.1025 \]
So we have:
\[ 1.1025 = \left(1 + \frac{R}{100}\right)^2 \]

### Step 6: Take the square root of both sides
Taking the square root gives:
\[ \sqrt{1.1025} = 1 + \frac{R}{100} \]
Calculating the square root:
\[ 1.05 = 1 + \frac{R}{100} \]

### Step 7: Isolate R
Now, subtract 1 from both sides:
\[ 1.05 - 1 = \frac{R}{100} \]
This simplifies to:
\[ 0.05 = \frac{R}{100} \]

### Step 8: Solve for R
To find R, multiply both sides by 100:
\[ R = 0.05 \times 100 \]
Thus:
\[ R = 5 \]

### Conclusion
The rate of interest is **5% per annum**.

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