Answer:
9 years , 11 months
Step-by-step explanation:
Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a year
Apply 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=2
t is number of years
A is the amount after t years= 9000
Plug 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=2t
Divide both sides by 2
t=9.91458
1 year = 12 months
0.91458 times 12 = 11
So 9 years , 11 months
