Compound Interest: Calculating Required Annual Rate

Compound interest is a crucial concept in the world of finance and investing. It refers to the interest that is calculated on both the initial principal and the interest that has been added to it over time. When interest is compounded continuously, the formula to calculate the future value of an investment is F = P * e^(r*t), where F is the future value, P is the principal amount, r is the interest rate, e is Euler's number, and t is the time in years.

In the scenario given, Judith puts $5000 into an investment account with the goal of growing it to $9110 after 30 years. To determine the approximate annual rate needed for this growth, we can rearrange the compound interest formula to solve for the interest rate:

Calculating Required Annual Rate:

r = ln(F/P) / t

Now, let's plug in the values we have:

r = ln(9110/5000) / 30

Therefore, the approximate annual interest rate needed for the investment account to reach $9110 after 30 years is the solution to the above equation.

Understanding compound interest and how it impacts investments is essential for making informed financial decisions. By knowing how to calculate the required annual rate for an investment to reach a specific goal, individuals can better plan and manage their investments for the future.