Answer:
It would take 12.1 years.
Step-by-step explanation:
We are given with $3000 invested in bank pays 6.75% interest compounded semi annually to the nearest 10th. We are asked to find the number of years the bank reaches $6700.
Let's use the compound interest formula.
[tex]A= P(1+\frac{r}{n}) ^{nt}[/tex]
We know A=6700
P=3000
r =0.0675
n=2(because compounded semiannually)
t =?( we need to find it)
Plug in the known values into the formula.
[tex]6700=3000(1+\frac{0.0675}{2}) ^{2*t}[/tex]
Simplify and solve for 't'
Divide both sides by 3000
[tex]2.23333= (1.03375)^{2t}[/tex]
Take log on both sides
[tex]log(2.23333) = 2t log(1.03375)[/tex]
Divide both sides by log(1.03375)
24.2067=2t
Divide both sides by 2.
t=12.10...
To round to nearest 10th, we get t=12.1 years.
