Question

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?

Answer 1

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.