The correct formula for this is as follows:
\(A=P(1+\frac{r}{n})^{nt}\)
where n is the number of compounding periods per year, and r is the annual interest rate as a decimal,
Plugging the given values into the formula, we get:
\(4550=2700(1+\frac{0.09}{4})^{4t}\)
This equation can be simplified to:
\(1.6852=(1.0225)^{4t}\)
Taking logs of both sides gives:
\(log 1.6852=4t\times log 1.0225\)
which can be rearranged to get:
\(t=\frac{log 1.6852}{4\times log 1.0225}=5.864\)
So it will take about 5.864 years for the amount to reach $4550.
