If the simple interest for 4 year be equal to 20% of the principal it will be equal to principal in how many year?

Options

A. 30 year
B. 25 year
C. 20 year
D. 23 year

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the information given in the question.

### Step 1: Understand the given information
We know that the simple interest for 4 years is equal to 20% of the principal amount (P).

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

### Step 3: Set up the equation based on the given information
From the question, we know:
\[ SI = 20\% \text{ of } P = \frac{20}{100} \times P = 0.2P \]
And since the time \(T\) is 4 years, we can substitute into the SI formula:
\[ 0.2P = \frac{P \times R \times 4}{100} \]

### Step 4: Simplify the equation
We can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ 0.2 = \frac{R \times 4}{100} \]
Now, multiply both sides by 100:
\[ 20 = R \times 4 \]
Now, divide both sides by 4:
\[ R = \frac{20}{4} = 5\% \]

### Step 5: Find out how many years it will take for the Simple Interest to equal the Principal
We need to find the time \(T\) when the Simple Interest equals the Principal.
Using the formula for SI again:
\[ SI = P \]
Substituting the SI formula:
\[ P = \frac{P \times R \times T}{100} \]
Cancelling \(P\) from both sides:
\[ 1 = \frac{R \times T}{100} \]
Now substitute \(R = 5\%\):
\[ 1 = \frac{5 \times T}{100} \]
Multiply both sides by 100:
\[ 100 = 5T \]
Now divide both sides by 5:
\[ T = \frac{100}{5} = 20 \text{ years} \]

### Final Answer
The time it will take for the Simple Interest to equal the Principal is **20 years**.

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