At what rate per cent of simple interest will the interest on Rs. 3,750 be one-fifth of itself in 4 years? To what will it amount in 15 years ?

Answer

To solve the problem step by step, we will break it down into two parts: finding the rate of simple interest and then calculating the amount after 15 years.

### Step 1: Identify the given values
- Principal (P) = Rs. 3,750
- Time (T) = 4 years
- Interest (I) = One-fifth of the principal

### Step 2: Calculate the interest
Since the interest is one-fifth of the principal:
\[ I = \frac{P}{5} = \frac{3750}{5} = 750 \]

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

### Step 4: Substitute the known values into the formula
We know:
- SI = 750
- P = 3750
- T = 4

Substituting these values into the formula:
\[ 750 = \frac{3750 \times R \times 4}{100} \]

### Step 5: Rearranging the equation to find R
To isolate R, we can rearrange the equation:
\[ 750 \times 100 = 3750 \times R \times 4 \]
\[ 75000 = 15000R \]
\[ R = \frac{75000}{15000} = 5 \]

### Step 6: Conclusion for the first part
The rate of simple interest is:
\[ R = 5\% \]

### Step 7: Calculate the amount after 15 years
Now, we need to calculate the amount after 15 years using the same formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- P = 3750
- R = 5
- T = 15

Substituting these values:
\[ SI = \frac{3750 \times 5 \times 15}{100} \]
\[ SI = \frac{281250}{100} = 2812.5 \]

### Step 8: Calculate the total amount
The total amount (A) is given by:
\[ A = P + SI \]
Substituting the values:
\[ A = 3750 + 2812.5 = 6562.5 \]

### Step 9: Conclusion for the second part
The amount after 15 years is:
\[ A = 6562.5 \]

### Final Answer:
1. The rate of simple interest is **5%**.
2. The amount after 15 years is **Rs. 6562.5**.

---