Seema invested an amount of Rs. 16000 for two years at compound interest and received an amount of Rs. 21160 on maturity. What is the rate of interest ?

Answer

To find the rate of interest for Seema's investment, we can use the formula for compound interest. The formula for the amount \( A \) after \( n \) years with principal \( P \) and rate \( r \) is given by:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \( A \) = Total amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

### Step 1: Identify the values
From the question:
- \( P = 16000 \) (the principal amount)
- \( A = 21160 \) (the amount received on maturity)
- \( n = 2 \) (the number of years)

### Step 2: Substitute the values into the formula
We can substitute the known values into the compound interest formula:

\[ 21160 = 16000 \left(1 + \frac{r}{100}\right)^2 \]

### Step 3: Divide both sides by 16000
To isolate the term with \( r \), divide both sides by 16000:

\[ \frac{21160}{16000} = \left(1 + \frac{r}{100}\right)^2 \]

Calculating the left side:

\[ \frac{21160}{16000} = 1.3225 \]

So, we have:

\[ 1.3225 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Take the square root of both sides
To eliminate the square, take the square root of both sides:

\[ \sqrt{1.3225} = 1 + \frac{r}{100} \]

Calculating the square root:

\[ 1.15 = 1 + \frac{r}{100} \]

### Step 5: Solve for \( r \)
Now, subtract 1 from both sides:

\[ 1.15 - 1 = \frac{r}{100} \]

\[ 0.15 = \frac{r}{100} \]

Multiply both sides by 100 to find \( r \):

\[ r = 0.15 \times 100 = 15 \]

### Conclusion
The rate of interest \( r \) is **15% per annum**.

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