sophie has $40 in an account. the interest rate is 5% compounded annually. to the nearest cent, how much…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=$40$, $r = 0.05$ (since $5%=0.05$), and $t = 3$.

Step2: Calculate the amount $A$

$A=40\times(1 + 0.05)^3=40\times(1.05)^3$. First, calculate $(1.05)^3=1.05\times1.05\times1.05 = 1.157625$. Then, $A = 40\times1.157625=46.305$.

Step3: Calculate the interest $I$

The interest $I$ is the difference between the final amount $A$ and the principal $P$. So, $I=A - P$. $I=46.305−40=$6.305$. Rounding to the nearest cent, $I\approx$6.31$.

Answer:

$6.31$