In how many years will Rs 1800 amount to Rs 2178 at 10% per annum when compounded annually?

Answer

To solve the problem of how many years it will take for Rs. 1800 to amount to Rs. 2178 at an interest rate of 10% per annum when compounded annually, we can use the formula for compound interest:

**Formula:**
\[ A = P \left(1 + \frac{R}{100}\right)^N \]

Where:
- \( A \) = Amount after time \( N \)
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( N \) = Number of years

**Step 1: Identify the values.**
- Principal amount \( P = 1800 \)
- Amount \( A = 2178 \)
- Rate of interest \( R = 10\% \)

**Step 2: Substitute the values into the formula.**
\[ 2178 = 1800 \left(1 + \frac{10}{100}\right)^N \]

**Step 3: Simplify the equation.**
\[ 2178 = 1800 \left(1 + 0.1\right)^N \]
\[ 2178 = 1800 \left(1.1\right)^N \]

**Step 4: Divide both sides by 1800 to isolate the exponential term.**
\[ \frac{2178}{1800} = (1.1)^N \]

**Step 5: Calculate the left side.**
\[ \frac{2178}{1800} = 1.21 \]
So, we have:
\[ 1.21 = (1.1)^N \]

**Step 6: Rewrite 1.21 as a power of 1.1.**
We know that:
\[ 1.1^2 = 1.21 \]
Thus, we can write:
\[ 1.21 = (1.1)^2 \]

**Step 7: Set the exponents equal to each other.**
Since the bases are the same, we can equate the exponents:
\[ N = 2 \]

**Conclusion:**
It will take **2 years** for Rs. 1800 to amount to Rs. 2178 at an interest rate of 10% per annum when compounded annually.

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