aaron wants to open a savings account. which account will grow his money the most? a. account 1: interest…

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 form), $n$ 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: Analyze Account 1

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

Step3: Analyze Account 2

For Account 2, $r_2=0.01$ and $n_2 = 365$ (compounded daily). Then $A_2=(1+\frac{0.01}{365})^{365}$. Since $r_1>r_2$, $A_1 > A_2$.

Step4: Analyze Account 3

For Account 3, $r_3=0.02$ and $n_3 = 12$ (compounded monthly). Then $A_3=(1+\frac{0.02}{12})^{12}$. Comparing with Account 1, since the more frequently compounded ( $n_1 = 365$ vs $n_3=12$) and with the same $r$, $A_1>A_3$.

Step5: Analyze Account 4

For Account 4, $r_4=0.01$ and $n_4 = 1$ (compounded annually). Then $A_4=(1 + 0.01)^{1}=1.01$. Clearly, $A_1$ is the largest among all.

Answer:

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