A sum of money doubles itself in 5 years at a certain rate of simple interest. W

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Question: A sum of money doubles itself in 5 years at a certain rate of simple interest. What is the rate?

Options:

Correct Answer: 10%

Solution:

If the principal doubles, SI = Principal. Rate = (SI / (Principal × Time)) × 100 = (Principal / (Principal × 5)) × 100 = 20%.

A sum of money doubles itself in 5 years at a certain rate of simple interest. What is the rate?

A sum of money doubles itself in 5 years at a certain rate of simple interest. What is the rate?

Step 1: Understand that the sum of money doubles in 5 years. This means if you start with a Principal amount (let's call it P), after 5 years, you will have 2P.
Step 2: Recognize that the amount of Simple Interest (SI) earned in this time is equal to the Principal (P) because 2P - P = P.
Step 3: Use the formula for Simple Interest: SI = (Principal × Rate × Time) / 100.
Step 4: Substitute SI with P, Principal with P, and Time with 5 years into the formula: P = (P × Rate × 5) / 100.
Step 5: Simplify the equation: P = (5P × Rate) / 100.
Step 6: Divide both sides by P (assuming P is not zero): 1 = (5 × Rate) / 100.
Step 7: Multiply both sides by 100: 100 = 5 × Rate.
Step 8: Divide both sides by 5 to find Rate: Rate = 100 / 5 = 20%.

Simple Interest – Understanding how simple interest is calculated and its relationship with principal, rate, and time.
Doubling Principle – Recognizing that if a sum of money doubles, the simple interest earned equals the principal.
Rate Calculation – Applying the formula for calculating the rate of interest based on simple interest.