Understanding Simple Interest
Simple interest is calculated using the formula:
Interest = Principal × Rate × Time
Where:
- Principal is the initial amount of money.
- Rate is the interest rate per year.
- Time is the number of years the money is invested or borrowed.
Doubling the Amount
To double an amount through simple interest in 20 years, the total amount after 20 years must equal twice the principal.
Setting Up the Equation
Let:
- Principal = P
- Total Amount after 20 years = 2P
- Interest earned over 20 years = Total Amount - Principal = 2P - P = P
Using the simple interest formula, we can set up the equation:
P = P × Rate × 20
Solving for Rate
Dividing both sides by P (assuming P is not zero):
1 = Rate × 20
Now, isolate the Rate:
Rate = 1 / 20
To convert this into a percentage:
Rate = (1 / 20) × 100 = 5%
Conclusion
To summarize, the rate at which an amount will double itself in 20 years at simple interest is:
- 5% per annum
This calculation illustrates the straightforward nature of simple interest and how time and rate interplay to achieve the desired return on investment.