12) $1,030 at 4% compounded semiannually for 2 years

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.

Step2: Convert values to appropriate form

Given $P=$1030$, $r = 0.04$ (since $4%=0.04$), $n = 2$ (compounded semiannually), and $t = 2$ years.

Step3: Substitute values into formula

$A=1030(1 +\frac{0.04}{2})^{2\times2}=1030(1 + 0.02)^{4}$.

Step4: Calculate the value inside the parentheses

$(1 + 0.02)^{4}=1.02^{4}=1.02\times1.02\times1.02\times1.02 = 1.08243216$.

Step5: Calculate the final amount

$A=1030\times1.08243216=$1114.9051248\approx$1114.91$.

Answer:

$$1114.91$