What sum of money will amount to `₹840` in `3` years at `4%` interest per year ?

Answer

To find the principal amount (P) that will amount to ₹840 in 3 years at an interest rate of 4% per annum, we can follow these steps:

### Step 1: Identify the given values
- Amount (A) = ₹840
- Time (T) = 3 years
- Rate of Interest (R) = 4%

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- P = Principal amount
- R = Rate of interest
- T = Time in years

### Step 3: Relate Simple Interest to Amount
The relationship between the amount, principal, and simple interest is given by:
\[ A = P + \text{SI} \]
This can be rewritten as:
\[ \text{SI} = A - P \]

### Step 4: Substitute the SI formula into the amount equation
We can substitute the SI formula into the equation:
\[ A - P = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 840 - P = \frac{P \times 4 \times 3}{100} \]

### Step 5: Simplify the equation
This simplifies to:
\[ 840 - P = \frac{12P}{100} \]
To eliminate the fraction, multiply the entire equation by 100:
\[ 84000 - 100P = 12P \]

### Step 6: Combine like terms
Now, combine the terms involving P:
\[ 84000 = 100P + 12P \]
\[ 84000 = 112P \]

### Step 7: Solve for P
Now, divide both sides by 112 to find P:
\[ P = \frac{84000}{112} \]
Calculating this gives:
\[ P = 750 \]

### Conclusion
The principal amount (P) that will amount to ₹840 in 3 years at 4% interest per annum is **₹750**.

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