In how many years will a sum of money double itself at 18.75% per annum simple interest?

### Concept & Doubling Sum When a sum of money doubles itself at simple interest, the accumulated interest is exactly equal to the principal amount. If Amount = $2P$, then Simple Interest = $2P - P = P$. $$Time = \frac{100 \times S.I.}{P \times R}$$ ### Step-by-Step Solution * Let Principal = $P$. * Since the sum doubles, S.I. = $P$. * Rate (R) = 18.75% = $18\frac{3}{4}$% = $\frac{75}{4}$% * Time (T) = $\frac{100 \times P}{P \times \left(\frac{75}{4}\right)}$ * T = $\frac{100 \times 4}{75}$ = $\frac{400}{75}$ = $\frac{16}{3}$ years. * $\frac{16}{3}$ years = $5\frac{1}{3}$ years. * Convert the fractional year to months: $\frac{1}{3} \times 12$ months = 4 months. * Total Time = 5 years 4 months. ### Exam Strategy & Shortcut For a sum to double, use the formula $T = \frac{100}{R}$. $T = \frac{100}{18.75}$. To quickly divide by 18.75, multiply numerator and denominator by 4: $\frac{400}{75} = \frac{16}{3} = 5$ years and 4 months. ### Common Pitfall Incorrectly converting the fractional part of the year into months. Remember to multiply the fraction by 12, not 10. (e.g., $5.33$ years is NOT 5 years 3 months). ### Final Answer Therefore, the correct answer is **5 years 4 months**.