Understanding the Problem
To find the rate of interest per annum where the simple interest becomes 2/5 of the amount in 10 years, we first need to clarify some terms.
Key Definitions
- Principal (P): The initial sum of money.
- Amount (A): The total money accumulated after interest, calculated as A = P + SI (where SI is Simple Interest).
- Simple Interest (SI): Calculated using the formula SI = (P * R * T) / 100, where R is the rate of interest per annum and T is the time in years.
Given Information
- Time (T): 10 years
- Simple Interest (SI): 2/5 of Amount (A)
Formulating the Equation
1. The amount after 10 years can be expressed as:
A = P + SI
2. According to the problem, SI = (2/5)A.
3. Therefore, substituting SI into the amount:
A = P + (2/5)A
Solving for Amount
1. Rearranging the equation gives:
(3/5)A = P
2. Thus, we can express A in terms of P:
A = (5/3)P
Calculating the Simple Interest
1. From the SI formula:
SI = (P * R * T) / 100
SI = (P * R * 10) / 100
2. Substituting SI into the equation, we have:
(2/5)A = (P * R * 10) / 100
3. Replacing A with (5/3)P:
(2/5)(5/3)P = (P * R * 10) / 100
Finding the Rate (R)
1. Simplifying the equation gives:
(2/3)P = (P * R * 10) / 100
2. Dividing both sides by P (assuming P is not zero):
(2/3) = (R * 10) / 100
3. Cross-multiplying to find R:
R = (2/3) * 10 = 20/3
4. Therefore, the rate of interest is approximately:
R = 6.67% per annum
Conclusion
The required rate of interest per annum is 6.67%. This demonstrates how simple interest can be calculated and understood in relation to the principal and amount over time.