How long will it take for a sum of money to grow from Rs 1600 to Rs 12000 if it is invested at 12.5% per annum simple interest ?

Options

A. 60 yrs
B. 52 yrs
C. 56 yrs
D. Can't be determined

Answer

To solve the problem of how long it will take for a sum of money to grow from Rs 1600 to Rs 12000 at a simple interest rate of 12.5% per annum, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 1600
- Amount (A) = Rs 12000
- Rate of interest (R) = 12.5%

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = A - P \]
Substituting the values:
\[ SI = 12000 - 1600 = 10400 \]

### Step 3: Use the Simple Interest formula to find Time (T)
The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
Rearranging the formula to find Time (T):
\[ T = \frac{SI \times 100}{P \times R} \]

### Step 4: Substitute the known values into the formula
Substituting SI = 10400, P = 1600, and R = 12.5:
\[ T = \frac{10400 \times 100}{1600 \times 12.5} \]

### Step 5: Calculate the denominator
Calculating the denominator:
\[ 1600 \times 12.5 = 20000 \]

### Step 6: Substitute the denominator back into the formula
Now substituting back:
\[ T = \frac{1040000}{20000} \]

### Step 7: Perform the division
Calculating the division:
\[ T = 52 \]

### Conclusion
Thus, it will take **52 years** for the sum of money to grow from Rs 1600 to Rs 12000 at a simple interest rate of 12.5% per annum.

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