In what time will Rs 1000 amount to Rs 1331 at 10% per annum, compounded annually?

Answer

To solve the problem step by step, we will use the formula for compound interest and the information provided in the question.

### Step 1: Identify the given values
- Principal (P) = Rs 1000
- Amount (A) = Rs 1331
- Rate of interest (R) = 10% per annum
- Time (n) = ? (This is what we need to find)

### Step 2: Use the formula for compound interest
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 1331 = 1000 \left(1 + \frac{10}{100}\right)^n \]
\[ 1331 = 1000 \left(1 + 0.1\right)^n \]
\[ 1331 = 1000 \left(1.1\right)^n \]

### Step 4: Divide both sides by 1000
To isolate the term with \( n \):
\[ \frac{1331}{1000} = (1.1)^n \]
\[ 1.331 = (1.1)^n \]

### Step 5: Express 1.331 and 1.1 in exponential form
We can express 1.331 as \( \left(\frac{11}{10}\right)^3 \) since:
\[ 1.331 = 11 \times 11 \times 11 / (10 \times 10 \times 10) = \frac{11^3}{10^3} \]

### Step 6: Set the exponents equal to each other
Now we have:
\[ \left(\frac{11}{10}\right)^3 = (1.1)^n \]

Since \( 1.1 = \frac{11}{10} \), we can equate the exponents:
\[ 3 = n \]

### Step 7: Conclusion
Thus, the time \( n \) is equal to 3 years.

### Final Answer:
The time required for Rs 1000 to amount to Rs 1331 at 10% per annum, compounded annually, is **3 years**.

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