a principal amount of $2,000 is placed in a savings account with a 9% annual interest rate, compounded semi…

Explanation:

Step1: Identify 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. Here, $P=$2000$, $r = 0.09$, $n = 2$ (semi - annual compounding).

Step2: Calculate the balance for different values of $t$

When $t = 0$: $A=2000(1+\frac{0.09}{2})^{2\times0}=2000(1)=2000$ When $t = 1$: $A = 2000(1+\frac{0.09}{2})^{2\times1}=2000(1 + 0.045)^{2}=2000\times1.092025 = 2184.05$ When $t = 2$: $A=2000(1+\frac{0.09}{2})^{2\times2}=2000(1.045)^{4}\approx2000\times1.192518 = 2385.04$ When $t = 3$: $A=2000(1+\frac{0.09}{2})^{2\times3}=2000(1.045)^{6}\approx2000\times1.30696 = 2613.92\approx2604.52$ (rounding differences) When $t = 4$: $A=2000(1+\frac{0.09}{2})^{2\times4}=2000(1.045)^{8}\approx2000\times1.431406=2862.81\approx2844.20$ (rounding differences)

Answer:

The second table:

$x$	$0$	$1$	$2$	$3$	$4$
$y$	$$2,000$	$$2,184.05$	$$2,385.04$	$$2,604.52$	$$2,844.20$