In how many years will Rs 6250 amount to Rs 7290 at 8% per annum, compounded annually?

Answer

To solve the problem of how many years it will take for Rs. 6250 to amount to Rs. 7290 at an interest rate of 8% per annum compounded annually, we can follow these steps:

### Step 1: Identify 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:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Time in years

### Step 2: Substitute the known values into the formula
From the question:
- \( A = 7290 \)
- \( P = 6250 \)
- \( r = 8 \)

Substituting these values into the formula gives:
\[ 7290 = 6250 \left(1 + \frac{8}{100}\right)^n \]

### Step 3: Simplify the equation
Calculate \( 1 + \frac{8}{100} \):
\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]

Now, the equation becomes:
\[ 7290 = 6250 (1.08)^n \]

### Step 4: Isolate \( (1.08)^n \)
To isolate \( (1.08)^n \), divide both sides by 6250:
\[ \frac{7290}{6250} = (1.08)^n \]

### Step 5: Calculate \( \frac{7290}{6250} \)
Perform the division:
\[ \frac{7290}{6250} = 1.1664 \]

So now we have:
\[ 1.1664 = (1.08)^n \]

### Step 6: Take logarithms to solve for \( n \)
To solve for \( n \), we can take the logarithm of both sides:
\[ \log(1.1664) = n \cdot \log(1.08) \]

### Step 7: Calculate \( n \)
Now, we can solve for \( n \):
\[ n = \frac{\log(1.1664)}{\log(1.08)} \]

Using a calculator:
- \( \log(1.1664) \approx 0.0718 \)
- \( \log(1.08) \approx 0.0334 \)

Now substituting these values:
\[ n \approx \frac{0.0718}{0.0334} \approx 2.15 \]

Since we are looking for the number of years, we round \( n \) to the nearest whole number:
\[ n \approx 2 \text{ years} \]

### Final Answer
Thus, it will take approximately **2 years** for Rs. 6250 to amount to Rs. 7290 at an interest rate of 8% per annum compounded annually.

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