Answer: 2.9 years
Explanation:To calculate the number of years it will take for an investment to grow at 24% compounded monthly, we need to use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the amount of money at the end of the investment period, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the annual interest rate is 24%, which is equivalent to a monthly interest rate of 2%. The number of times the interest is compounded per year is 12 (monthly). Therefore, the formula becomes A = P(1 + 0.02/12)^(12t).
To find the number of years it will take for the investment to double, we need to set A/P = 2. Therefore, the formula becomes 2 = (1 + 0.02/12)^(12t). Solving for t, we get t = log(2)/(12*log(1 + 0.02/12)) = 35.0 months, or approximately 2.9 years.
Therefore, it will take approximately 2.9 years for the investment to double at 24% compounded monthly.