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 amount at the end of the third year.

Answer

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

### Step 1: Identify the given values
- Principal (P) = Rs. 7000
- Amount after 1 year (A) = Rs. 7980
- Time (n) = 1 year

### Step 2: Use the formula for compound interest
The formula for the amount after n years with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- A = Amount after n years
- P = Principal
- R = Rate of interest
- n = Number of years

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula for the first year:
\[ 7980 = 7000 \left(1 + \frac{R}{100}\right)^1 \]

### Step 4: Simplify the equation
Dividing both sides by 7000:
\[ \frac{7980}{7000} = 1 + \frac{R}{100} \]
\[ 1.14 = 1 + \frac{R}{100} \]

### Step 5: Solve for R
Subtracting 1 from both sides:
\[ 0.14 = \frac{R}{100} \]
Multiplying both sides by 100:
\[ R = 14\% \]

### Step 6: Calculate the amount at the end of the third year
Now that we have the rate of interest, we can calculate the amount at the end of the third year using the same formula:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Substituting the values:
\[ A = 7000 \left(1 + \frac{14}{100}\right)^3 \]
\[ A = 7000 \left(1.14\right)^3 \]

### Step 7: Calculate \( (1.14)^3 \)
Calculating \( (1.14)^3 \):
\[ (1.14)^3 \approx 1.4815 \]

### Step 8: Final calculation for A
Now substituting back:
\[ A = 7000 \times 1.4815 \]
\[ A \approx 10370.80 \]

### Final Answer
The amount at the end of the third year is approximately Rs. 10,370.80.

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