xin invested $400 in an account paying an interest rate of 5.3% compounded continuously. assuming no…

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal form

The interest rate $r = 5.3%=0.053$, $P = 400$, and $t = 13$.

Step3: Substitute the values into the formula

$A=400\times e^{0.053\times13}$. First, calculate the exponent: $0.053\times13 = 0.689$. Then, find $e^{0.689}$. Using a calculator, $e^{0.689}\approx1.991$. Now, $A = 400\times1.991$. $A = 796.4$.

Answer:

$796$