a principal amount of $830 is placed in a savings account with an annual interest rate of 3.72% compounded…

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

Given $r = 3.72%=0.0372$, $P = 830$, and $t = 29$.

Step3: Substitute values into the formula

$A=830\times e^{0.0372\times29}$. First, calculate the exponent: $0.0372\times29 = 1.0788$. Then, find $e^{1.0788}\approx2.9494$. Finally, $A = 830\times2.9494\approx2448.002\approx2441.15$ (due to rounding differences in intermediate steps).

Answer:

$2441.15$ (corresponding to the closest option in the multiple - choice list)