Answer:
We can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where: A = final amount (9,000 dollars) P = principal amount (3,000 dollars) r = annual interest rate (45% or 0.45) n = number of times compounded per year (12 for monthly) t = time in years (unknown)
Plugging in the values, we get:
9,000 = 3,000 * (1 + 0.45/12)^(12*t)
Simplifying:
3 = (1 + 0.45/12)^(12*t)
Taking the natural log of both sides:
ln(3) = 12*t * ln(1 + 0.45/12)
Dividing both sides by 12 * ln(1 + 0.45/12):
t = ln(3) / (12 * ln(1 + 0.45/12)) t = 2.16 years (to two decimal places)
Therefore, it will take approximately 2.16 years for the investment of 3,000 dollars to grow to 9,000 dollars at an interest rate of 45% per year, compounded monthly.