A man invest rupes 7,000 for three years , at a certain rate of interest , compounded annually At the end of one year it amount rupes 7,980 Calculate
the rate of interest per annum

Answer

To solve the problem step by step, we will use the formula for compound interest. The formula for the amount \( A \) after \( n \) years with principal \( P \) and rate of interest \( r \) is given by:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

### Step 1: Identify the given values
- Principal \( P = 7000 \) rupees
- Amount after 1 year \( A = 7980 \) rupees
- Time \( n = 1 \) year (since we are calculating the rate for the first year)

### Step 2: Substitute the values into the formula
We substitute the known values into the compound interest formula:

\[ 7980 = 7000 \left(1 + \frac{r}{100}\right)^1 \]

### Step 3: Simplify the equation
Now, we can simplify the equation:

\[ 7980 = 7000 \left(1 + \frac{r}{100}\right) \]

### Step 4: Divide both sides by 7000
To isolate the term with \( r \), we divide both sides by 7000:

\[ \frac{7980}{7000} = 1 + \frac{r}{100} \]

Calculating the left side:

\[ \frac{7980}{7000} = 1.140 \]

So, we have:

\[ 1.140 = 1 + \frac{r}{100} \]

### Step 5: Solve for \( r \)
Now, we subtract 1 from both sides:

\[ 1.140 - 1 = \frac{r}{100} \]

\[ 0.140 = \frac{r}{100} \]

Now, multiply both sides by 100 to find \( r \):

\[ r = 0.140 \times 100 = 14 \]

### Step 6: Conclusion
The rate of interest per annum is:

\[ \boxed{14\%} \]