Arturo invests $2700 in a savings account that pay 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550?
The correct formula for this is as follows: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] 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: [tex]4550=2700(1+\frac{0.09}{4})^{4t}[/tex] This equation can be simplified to: [tex]1.6852=(1.0225)^{4t}[/tex] Taking logs of both sides gives: [tex]log 1.6852=4t\times log 1.0225[/tex] which can be rearranged to get: [tex]t=\frac{log 1.6852}{4\times log 1.0225}=5.864[/tex] So it will take about 5.864 years for the amount to reach $4550.
