you have $12,000 to invest and want to keep your money invested for 8 years. you are considering the…

Explanation:

Step1: Recall compound - interest and simple - interest formulas

Compound - interest formula: $A = P(1+\frac{r}{n})^{nt}$, 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. Simple - interest formula: $A=P(1 + rt)$. Given $P=$12000$ and $t = 8$ years.

Step2: Calculate the amount for option a

$r_a=0.0399$, $n_a = 12$. $A_a=12000(1+\frac{0.0399}{12})^{12\times8}=12000(1 + 0.003325)^{96}=12000\times1.003325^{96}\approx12000\times1.3777\approx$16532.4$

Step3: Calculate the amount for option b

$r_b = 0.04$, $n_b=4$. $A_b=12000(1+\frac{0.04}{4})^{4\times8}=12000(1 + 0.01)^{32}=12000\times1.01^{32}\approx12000\times1.3749\approx$16498.8$

Step4: Calculate the amount for option c

$r_c=0.04175$, $n_c = 1$. $A_c=12000(1 + 0.04175)^{8}=12000\times1.04175^{8}\approx12000\times1.3887\approx$16664.4$

Step5: Calculate the amount for option d

$r_d=0.042$. $A_d=12000(1+0.042\times8)=12000(1 + 0.336)=12000\times1.336=$16032$

Answer:

C. $4.175%$ compounded annually