At what rate percent per annum compound interest, with Rs 10,000 amount to Rs 13,310 in three years ?

Options

A. `8%`
B. `10%`
C. `12%`
D. `15%`

Answer

To solve the problem of finding the rate percent per annum compound interest that turns Rs 10,000 into Rs 13,310 in three years, we can follow these steps:

### Step 1: Understand the formula for compound interest
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( A \) = final amount (Rs 13,310)
- \( P \) = principal amount (Rs 10,000)
- \( r \) = rate of interest per annum (unknown)
- \( n \) = number of years (3 years)

### Step 2: Substitute the known values into the formula
We substitute \( A = 13,310 \), \( P = 10,000 \), and \( n = 3 \) into the formula:
\[ 13,310 = 10,000 \left(1 + \frac{r}{100}\right)^3 \]

### Step 3: Simplify the equation
To simplify, divide both sides by 10,000:
\[ \frac{13,310}{10,000} = \left(1 + \frac{r}{100}\right)^3 \]
This simplifies to:
\[ 1.331 = \left(1 + \frac{r}{100}\right)^3 \]

### Step 4: Take the cube root of both sides
To isolate \( 1 + \frac{r}{100} \), take the cube root of both sides:
\[ 1 + \frac{r}{100} = \sqrt[3]{1.331} \]

### Step 5: Calculate the cube root
Calculating the cube root, we find:
\[ 1 + \frac{r}{100} \approx 1.1 \]

### Step 6: Solve for \( r \)
Now, isolate \( r \):
\[ \frac{r}{100} = 1.1 - 1 \]
\[ \frac{r}{100} = 0.1 \]

Now, multiply both sides by 100:
\[ r = 0.1 \times 100 \]
\[ r = 10 \]

### Conclusion
The rate of interest \( r \) is 10%.