Part A Which account will have a greater value after 10 years? What will the value be? \[ \begin{array}{l}\text { Account } \mathrm{A}\end{array} \] \( \begin{array}{l}\text { Account B } \\ \text { principal: } \$ 16,000\end{array} \) \( \begin{array}{l}\text { annual interest: } 3 \% \\ \text { compounded quarterly } \\ \text { number of years: } 10\end{array} \) \( \begin{array}{l}\text { principal: } \$ 16,000 \\ \text { annual interest: } 3 \% \\ \text { compounded monthly } \\ \text { number of years: } 10\end{array} \) Account \( \begin{array}{l}\text { Choose... }\end{array} \) Part B What type of growth do both accounts model? A. linear most after 10 years. It will have a value of \( \$ \) Choose... B. exponential C neither

To find the greater value after 10 years for each account, we can utilize the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] For Account A (compounded quarterly): - Principal, \( P = 16,000 \) - Annual interest rate, \( r = 0.03 \) - Number of times interest applied per year, \( n = 4 \) - Total number of years, \( t = 10 \) Calculating gives us: \[ A_A = 16,000 \left(1 + \frac{0.03}{4}\right)^{4 \times 10} \approx 16,000 \times (1.0075)^{40} \approx 16,000 \times 1.34885 \approx 21,581.60 \] For Account B (compounded monthly): - Principal, \( P = 16,000 \) - Annual interest rate, \( r = 0.03 \) - Number of times interest applied per year, \( n = 12 \) Calculating gives us: \[ A_B = 16,000 \left(1 + \frac{0.03}{12}\right)^{12 \times 10} \approx 16,000 \times (1.0025)^{120} \approx 16,000 \times 1.34935 \approx 21,589.60 \] So for part A, both accounts will yield approximately \( \$21,581.60 \) for Account A and \( \$21,589.60 \) for Account B, meaning Account B has a slightly greater value after 10 years. Now for part B, both accounts model B. exponential growth due to interest compounding over time. This means your money isn't just earning interest on itself, but also generating interest on the interest! Fun, right? It's how money grows in a "magical" way! So, the answer for the type of growth is B. exponential.