13) Ms. Timarky deposits \( \$ 300 \) in an account that earns simple interest at an annual rate of \( 2 \% \). Ms. Waugh deposits \( \$ 300 \) in an account that earns \( 2 \% \) interest and is compounded annually. After 5 years, who has more money in their account and why?

After 5 years, Ms. Timarky's account will have earned simple interest calculated as follows: Interest = Principal x Rate x Time = \( 300 \times 0.02 \times 5 = \$30 \). So, her total amount will be \( 300 + 30 = \$330 \). On the other hand, Ms. Waugh's account will earn compounded interest. The formula for compound interest is: Total Amount = Principal x (1 + Rate)^Time = \( 300 \times (1 + 0.02)^5 \). Calculating this gives: Total Amount = \( 300 \times (1.02)^5 \approx 300 \times 1.10408 \approx \$331.22 \). Thus, Ms. Waugh has more money in her account after 5 years at approximately \( \$331.22 \), compared to Ms. Timarky's \( \$330 \), because compounding allows her interest to earn interest over time. The dynamic of interest—simple versus compound—shows how compounding can significantly enhance savings in the long run! Many people underestimate the power of starting with even a modest sum and letting it grow with compound interest. Investing early and wisely can lead to a fruitful financial future!