\( \begin{array}{ll}\text { estion } 2 \text { (4 points) } \\ & \\ \text { Hor graduation, Emma receives } \$ 875 \text { from the money in the cards she received from family } \\ \text { and friends. } \\ \text { How would it take for Emma's money to double (grow to } \$ 1750 \text { ) if the interest is } \\ \text { compounded continuously at } 6 \% ?\end{array} \)

To determine how long it will take for Emma's money to double under continuously compounded interest, we can use the formula for continuous compound interest: \( A = Pe^{rt} \). Here, \( A \) is the amount of money accumulated after time \( t \), \( P \) is the principal amount (in this case, $875), \( r \) is the annual interest rate (0.06), and \( t \) is the time in years. Setting \( A \) to $1750 gives us the equation \( 1750 = 875e^{0.06t} \). Dividing both sides by 875 gives \( 2 = e^{0.06t} \). Taking the natural logarithm of both sides allows us to solve for \( t \): \( \ln(2) = 0.06t \), leading to \( t \approx \frac{\ln(2)}{0.06} \approx 11.55 \) years. So, Emma can expect her money to double in about 11.55 years! Now, to spice things up, if Emma were to invest her money in a high-interest savings account instead, she might achieve faster growth with features like a sign-up bonus or higher rates for large deposits. However, remember that while it can be tempting to chase high yields, it’s crucial to assess the reliability and safety of such investments, evaluating terms and conditions carefully!