Elena is thinking about putting $200 in a savings account that earns 4% interest compounded semiannually. She wants to keep that money in the account for 4 years. Which of the formulas below can help her calculate how much money she will have at the end of the 4 years? A. $200(1 + 0.02)8 B. $200(1 + 0.04)4 C. $200(1 + 0.02)4 D. $200(1 + 0.08)2

Answer:A. [tex]\$200(1 + 0.02)^8[/tex]Step-by-step explanation:Since, the amount that compounded semiannually is,[tex]A=P(1+\frac{r}{2})^{2t}[/tex]Where, P is the principal amount,r is the annual rate ( in decimals ),And, t is time ( in years ),Here, P = $ 200,r = 4 % = 0.04    ( 1 % = 0.01 ),t = 4 years,Hence, the amount after 4 years would be,[tex]A=200(1+\frac{0.04}{2})^{2\times 4}[/tex][tex]=200(1+0.02)^8[/tex]⇒ First option is correct.