the table shows the account information of five investors. which of the following are true, assuming no…

Explanation:

Step1: Recall compound - interest formulas

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

Step2: Calculate for Steve

$P = 3800$, $r=0.035$, $n = 2$ (semi - annually), $t = 20$. $A=3800(1 +\frac{0.035}{2})^{2\times20}=3800(1 + 0.0175)^{40}\approx3800\times2.0076 = 7628.88\approx7629$.

Step3: Calculate for Tara

$P = 2100$, $r = 0.045$, compounded continuously, $t=6$. $A=2100e^{0.045\times6}=2100e^{0.27}\approx2100\times1.3100 = 2751\approx2750.93$.

Step4: Calculate for Lon

$P = 7200$, $r = 0.05$, $n = 1$ (annually), $t = 15$. $A=7200(1 + 0.05)^{15}=7200\times2.0789 = 14968.08$.

Step5: Calculate for Nick

$P = 2500$, $r = 0.03$, $n = 4$ (quarterly), $t = 8$. $A=2500(1+\frac{0.03}{4})^{4\times8}=2500(1 + 0.0075)^{32}\approx2500\times1.2709 = 3177.25\approx3177.17$.

Step6: Calculate for Anna

$P = 4000$, $r = 0.015$, $n = 12$ (monthly), $t = 12$. $A=4000(1+\frac{0.015}{12})^{12\times12}=4000(1+\frac{0.015}{12})^{144}\approx4000\times1.2493=4997.2$.

Answer:

A. After 15 years, Lon will have about $14968.08$ (not about $15218.67$). B. After 12 years, Anna will have about $4997.2$ (not about $4788.33$). C. After 6 years, Tara will have about $2750.93$ (correct). D. After 8 years, Nick will have about $3177.17$ (correct). E. After 20 years, Steve will have about $7629$ (correct). So the correct answers are C, D, E.