question 10 / 10\naaron wants to open a savings account. which account will grow his money the most?\na…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. For simplicity, assume $P = 1$ and $t = 1$.

Step2: Calculate for Account 1

For Account 1 with $r_1=0.02$ and $n_1 = 365$ (compounded daily), $A_1=(1 +\frac{0.02}{365})^{365}\approx1.0202$.

Step3: Calculate for Account 2

For Account 2 with $r_2 = 0.01$ and $n_2=365$ (compounded daily), $A_2=(1+\frac{0.01}{365})^{365}\approx1.0101$.

Step4: Calculate for Account 3

For Account 3 with $r_3 = 0.02$ and $n_3 = 12$ (compounded monthly), $A_3=(1+\frac{0.02}{12})^{12}\approx1.0202$. But $(1+\frac{0.02}{365})^{365}>(1+\frac{0.02}{12})^{12}$ since more compounding periods lead to more growth when the interest rate is the same.

Step5: Calculate for Account 4

For Account 4 with $r_4 = 0.01$ and $n_4 = 1$ (compounded annually), $A_4=1 + 0.01=1.01$.

Answer:

A. Account 1: Interest rate 2%, interest compounded daily.