Question 1 Mark this question If \( \$ 15,000 \) is invested at \( 6.5 \% \) annual interest compounded annually, how long would it take for the account balance to reach \( \$ 50,000 \) ? Round your answer to the nearest tenth. 19.1 years 22.5 years 17.3 years 25.9 years SAVE \& CONTINUE

To solve this problem, you can use the formula for compound interest: \[ A = P (1 + r)^t \] Where \( A \) is the amount of money accumulated after n years, including interest. \( P \) is the principal amount (the initial amount of money), \( r \) is the annual interest rate (decimal), and \( t \) is the time in years. Here, you would set \( A = 50,000 \), \( P = 15,000 \), and \( r = 0.065 \). To find \( t \), rearranging the formula gives: \[ t = \frac{\log(A/P)}{\log(1 + r)} \] Plugging in the values, you get: \[ t = \frac{\log(50,000 / 15,000)}{\log(1 + 0.065)} \approx 19.1 \text{ years} \] This gentle reminder is that when it comes to money management, knowledge of compound interest can take you from a small investment to a potentially large sum over time! If you’ve ever seen your favorite movie sequel, you know that sometimes it's the journey that counts! Compound interest isn't just about numbers; it's about the growth of your investment seemingly without you even noticing! So, keep those calculations handy for future fiscal fun!