A sum of money trebles (i.e., 3 times) in 15 years at r% of simple interest per annum . What is the value of r ?

Options

A. `12%`
B. `40/3%`
C. `(50)/3%`
D. can't be determined.

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Problem
We are given that a sum of money triples in 15 years at a certain rate of simple interest, r%. We need to find the value of r.

### Step 2: Define the Variables
Let the principal amount (initial sum of money) be \( P = x \). Since the amount triples, the total amount after 15 years will be:
\[ A = 3x \]

### Step 3: Calculate the Simple Interest
The simple interest (SI) can be calculated using the formula:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 3x - x = 2x \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest is:
\[ SI = \frac{P \cdot r \cdot t}{100} \]
Where:
- \( SI \) is the simple interest,
- \( P \) is the principal,
- \( r \) is the rate of interest,
- \( t \) is the time in years.

Substituting the known values into the formula:
\[ 2x = \frac{x \cdot r \cdot 15}{100} \]

### Step 5: Simplify the Equation
We can simplify the equation by canceling \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 2 = \frac{r \cdot 15}{100} \]

### Step 6: Solve for r
Now, we can solve for \( r \) by multiplying both sides by 100:
\[ 200 = r \cdot 15 \]
Now, divide both sides by 15:
\[ r = \frac{200}{15} \]
Simplifying this gives:
\[ r = \frac{40}{3} \approx 13.33\% \]

### Final Answer
The value of \( r \) is \( \frac{40}{3}\% \) or approximately \( 13.33\% \).

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