Seema invested an amount of 16,000 for two years on compound interest and received an amount of 17,640 on maturity. What is the rate of interest ?

Options

A. `5%` pa
B. `8%` pa
C. `4%` pa
D. Data inadequate

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 is given by:

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

Where:
- \( A \) = final amount (maturity amount)
- \( P \) = principal amount (initial investment)
- \( r \) = rate of interest per annum
- \( n \) = number of years

Given:
- \( A = 17,640 \)
- \( P = 16,000 \)
- \( n = 2 \)

### Step 1: Substitute the known values into the formula

\[ 17,640 = 16,000 \left(1 + \frac{r}{100}\right)^2 \]

### Step 2: Divide both sides by 16,000

\[ \frac{17,640}{16,000} = \left(1 + \frac{r}{100}\right)^2 \]

Calculating the left side:

\[ \frac{17,640}{16,000} = 1.1025 \]

So we have:

\[ 1.1025 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 3: Take the square root of both sides

\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]

Calculating the square root:

\[ 1.05 = 1 + \frac{r}{100} \]

### Step 4: Subtract 1 from both sides

\[ 1.05 - 1 = \frac{r}{100} \]

This simplifies to:

\[ 0.05 = \frac{r}{100} \]

### Step 5: Multiply both sides by 100 to find \( r \)

\[ r = 0.05 \times 100 \]

Calculating this gives:

\[ r = 5 \]

### Conclusion

The rate of interest \( r \) is **5%**.

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