The minimum number of half years in which a sum of money kept at 60% compound…

Step-by-Step Solution

To determine the minimum number of half-years required for a sum of money to quadruple at a 60% annual compound interest rate, we need to track the growth of the investment.

1. Understand the terms:

   • Annual interest rate = 60%.

   • Compounding frequency = Half-yearly.

   • Semi-annual interest rate = 60% / 2 = 30%.

   • Target amount = 4 * Principal.

2. Track the growth period by period:

   • Let the Principal (P) = 100. We want the Amount (A) to reach 400.

   • Period 1 (first half-year): 100 + (30% of 100) = 130

   • Period 2 (second half-year): 130 + (30% of 130) = 130 + 39 = 169

   • Period 3 (third half-year): 169 + (30% of 169) = 169 + 50.7 = 219.7

   • Period 4 (fourth half-year): 219.7 + (30% of 219.7) = 219.7 + 65.91 = 285.61

   • Period 5 (fifth half-year): 285.61 + (30% of 285.61) = 285.61 + 85.68 = 371.29

   • Period 6 (sixth half-year): 371.29 + (30% of 371.29) = 371.29 + 111.39 = 482.68

3. Conclusion:

   • By the end of 5 half-years, the amount is 371.29 (less than 400).

   • By the end of 6 half-years, the amount is 482.68 (more than 400).

   • Therefore, the minimum number of half-years required to reach or exceed quadrupling is 6.