Calculating the Time Required for a Sum of Money to Become Four Times at 12% p.a. Simple Interest

To calculate the time required for a sum of money to become four times at 12% p.a. simple interest, we can use the formula for simple interest:

Simple Interest = (Principal × Rate × Time) / 100

In this case, the principal is the initial sum of money, the rate is 12% p.a. (per annum), and the time is what we need to find. Let's break down the process step by step:

Step 1: Understand the problem
We are given that the sum of money needs to become four times its initial value. We also know the rate of interest, which is 12% p.a. Our goal is to calculate the time required for this growth to occur.

Step 2: Identify the known values
Principal (initial sum of money) = P
Rate of interest = R = 12% = 0.12
Final amount = 4P

Step 3: Set up the formula
Using the formula for simple interest, we can rearrange it to find the time:
Time = (Simple Interest × 100) / (Principal × Rate)

Step 4: Calculate the simple interest
The simple interest is the difference between the final amount and the principal:
Simple Interest = Final amount - Principal = 4P - P = 3P

Step 5: Substitute the values and calculate the time
Now, let's substitute the known values into the formula and calculate the time:
Time = (3P × 100) / (P × 0.12) = 25 years

Step 6: Interpret the result
Therefore, it will take 25 years for the sum of money to become four times its initial value at a 12% p.a. simple interest rate.

In conclusion, by using the formula for simple interest and substituting the known values, we determined that it would take 25 years for a sum of money to become four times its initial value at a 12% p.a. simple interest rate.