Final answer:
To triple the principal money in an account with continuous compounding at a 4.5% annual interest rate, it will take approximately 15.3625 years.
Step-by-step explanation:
To calculate the time it takes to triple the principal money in an account with continuous compounding, we can use the formula A = P * e^(rt), where A is the future value, P is the principal, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years. In this case, we want to find t, so we rearrange the formula to t = ln(A/P) / r.
Given that we want to triple the principal, the future value A would be 3 times the principal P. The annual interest rate r is 4.5%, or 0.045 in decimal form. Plugging in the values, we get t = ln(3) / 0.045. Using a calculator, we find that t is approximately 15.3625 years.
Therefore, it will take approximately 15.3625 years to triple the principal money in an account that pays a 4.5% annual interest rate compounded continuously.