Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it take for the account to be worth $9,000? (3 points)Select one:a. 21 years, 1 monthb. 18 years, 0 monthsc. 19 years, 10 monthsd. 9 years, 11 months

Answer:9 years , 11 monthsStep-by-step explanation:Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a yearApply compound interest formula[tex]A= P(1+\frac{r}{n})^{nt}[/tex]Where  P is the initial amount=$5,960.32'r' is the rate of interest=4.2%=0.042'n' is the compounding period=2t is number of yearsA is the amount after t years= 9000Plug in all the values in the formula[tex]9000=5960.32(1+\frac{0.042}{2})^{2t}[/tex]Divide both sides by 5960.32[tex]\frac{9000}{5960.32} =(1.021)^{2t}[/tex]Take ln on both sides[tex]ln(\frac{9000}{5960.32}) =ln((1.021)^{2t})[/tex][tex]ln(\frac{9000}{5960.32}) =2tln((1.021))[/tex]Now divide both sides by ln(1.021)19.82916538=2tDivide both sides by 2t=9.914581 year = 12 months0.91458 times 12 = 11So 9 years , 11 months