A sum of money invested at simple interest triples itself in 8 years. How many times will it become in 20 years time?

Options

A. 8 times
B. 7 times
C. 6 times
D. 9 times

Answer

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

### Step 1: Understand the Problem
We know that a sum of money triples itself in 8 years at simple interest. We need to find out how many times it will become in 20 years.

### Step 2: Define Variables
Let the principal amount (initial investment) be \( P \). According to the problem, the amount triples in 8 years. Therefore, the total amount after 8 years is:
\[ A = 3P \]

### Step 3: Calculate Simple Interest
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) is the simple interest,
- \( P \) is the principal,
- \( R \) is the rate of interest,
- \( T \) is the time in years.

Since the amount after 8 years is \( 3P \), we can express the simple interest as:
\[ SI = A - P = 3P - P = 2P \]

### Step 4: Set Up the Equation
Now we can set up the equation using the simple interest formula:
\[ 2P = \frac{P \times R \times 8}{100} \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 8}{100} \]

### Step 6: Solve for Rate \( R \)
Now, we can solve for \( R \):
\[ R \times 8 = 200 \implies R = \frac{200}{8} = 25\% \]

### Step 7: Calculate Simple Interest for 20 Years
Now we need to find out how much the amount will be after 20 years. Using the same formula for simple interest:
\[ SI_{20} = \frac{P \times R \times 20}{100} \]
Substituting \( R = 25\% \):
\[ SI_{20} = \frac{P \times 25 \times 20}{100} = \frac{500P}{100} = 5P \]

### Step 8: Calculate Total Amount After 20 Years
The total amount after 20 years will be:
\[ A_{20} = P + SI_{20} = P + 5P = 6P \]

### Step 9: Determine How Many Times the Principal Amount
To find out how many times the principal amount \( P \) it has become, we can express it as:
\[ \text{Times} = \frac{A_{20}}{P} = \frac{6P}{P} = 6 \]

### Final Answer
Thus, the amount will become **6 times** the principal in 20 years.

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