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 will have earned simple interest on her deposit. The simple interest formula is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the rate (expressed as a decimal), and \( t \) is the time in years. Plugging in the numbers gives \( I = 300 \times 0.02 \times 5 = 30 \). So, she will have \( 300 + 30 = 330 \) dollars. On the other hand, Ms. Waugh’s account earns compound interest. The compound interest formula is \( A = P(1 + r)^t \). For her, this yields \( A = 300(1 + 0.02)^5 \), which is approximately \( 300 \times 1.10408 = 331.22 \) dollars. Therefore, after 5 years, Ms. Waugh has more money in her account because compounding allows interest to earn interest over time, leading to a higher total than simple interest.