₹6000 becomes ₹7200 in 3 years at a certain rate of compound interest. What will be the amount received after 9 years?

Options

A. ₹11,498
B. ₹10,352
C. ₹9,368
D. ₹10,368

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Given Values
- Principal (P) = ₹6000
- Amount after 3 years (A) = ₹7200
- Time (t) = 3 years

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

### Step 3: Substitute the Known Values
Substituting the known values into the formula:
\[ 7200 = 6000 \left(1 + \frac{r}{100}\right)^3 \]

### Step 4: Simplify the Equation
Dividing both sides by 6000:
\[ \frac{7200}{6000} = \left(1 + \frac{r}{100}\right)^3 \]
\[ 1.2 = \left(1 + \frac{r}{100}\right)^3 \]

### Step 5: Take the Cube Root
To find \(1 + \frac{r}{100}\), take the cube root of both sides:
\[ 1 + \frac{r}{100} = (1.2)^{\frac{1}{3}} \]

### Step 6: Calculate the Cube Root
Calculating the cube root of 1.2:
\[ 1 + \frac{r}{100} \approx 1.063 \]
Thus,
\[ \frac{r}{100} \approx 0.063 \]
So,
\[ r \approx 6.3\% \]

### Step 7: Find the Amount After 9 Years
Now we need to find the amount after 9 years using the same formula:
\[ A = 6000 \left(1 + \frac{r}{100}\right)^9 \]
Substituting \(r \approx 6.3\%\):
\[ A = 6000 \left(1.063\right)^9 \]

### Step 8: Calculate \((1.063)^9\)
Calculating \((1.063)^9\):
\[ (1.063)^9 \approx 1.747 \]

### Step 9: Calculate the Final Amount
Now substitute back into the amount formula:
\[ A \approx 6000 \times 1.747 \]
\[ A \approx 10482 \]

### Final Answer
The amount received after 9 years is approximately **₹10,482**.

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