Understanding Simple Interest
Simple interest (SI) is calculated using the formula:
SI = (Principal × Rate × Time) / 100
Where:
- Principal is the initial sum of money.
- Rate is the interest rate per annum.
- Time is the duration in years.
Given Condition
In this scenario, the principal amount doubles in 5 years. This means:
- Final Amount (A) = 2 × Principal (P)
The relationship can be expressed as:
A = P + SI
Calculating Simple Interest
Since the amount doubles in 5 years:
- 2P = P + SI
- SI = P
Now, substituting SI in the formula:
P = (P × Rate × 5) / 100
Solving for Rate
To find the rate, rearranging the equation gives:
Rate = (100 × SI) / (Principal × Time)
Substituting SI with P and Time with 5 years results in:
Rate = (100 × P) / (P × 5)
This simplifies to:
Rate = 100 / 5
Final Calculation
Thus, the rate of simple interest is:
Rate = 20%
Conclusion
The rate of simple interest that causes a certain sum of money to double in 5 years is 20% per annum. This indicates a healthy return on investment for such a time frame.