A sum becomes its double in $10$ years. Find the annual rate of simple interest.

Question

Accepted Answer

Concept & Sum Multipliers: When a sum becomes "n" times itself, the simple interest earned is equal to (n-1) times the original principal. R = ((n - 1) × 100/T) Step-by-Step Solution: - Let the principal sum be P. - The sum doubles, so the Amount (A) = 2P. - Simple Interest (SI) = Amount - Principal = 2P - P = P. - Time (T) = 10 years. - Using the standard SI formula: - SI = (P × R × T/100) - P = (P × R × 10/100) - 1 = (R × 10/100) - 1 = (R/10) - R = 10% Exam Strategy & Shortcut: If money doubles, it means the interest earned is exactly 100% of the principal. To find the rate, simply divide this 100% by the number of years: (100/10) = 10%. Common Pitfall: A common error is to set the interest equal to 2P instead of the amount being 2P, leading to double the actual interest rate. Final Answer: Therefore, the correct answer is 10%.

Simple Interest Questions

Questions

Practice smarter