eva invested $31,000 in an account paying an interest rate of 3.8% 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 $r = 3.8%=0.038$. The principal amount $P = 31000$, and the number of years $t = 20$.

Step3: Substitute the values into the formula

Substitute $P = 31000$, $r=0.038$, and $t = 20$ into the formula $A = Pe^{rt}$. So $A=31000\times e^{0.038\times20}$.

Step4: Calculate the exponent

First, calculate $0.038\times20 = 0.76$. Then, find the value of $e^{0.76}$. Using a calculator, $e^{0.76}\approx2.1387$.

Step5: Calculate the final amount

Multiply $31000$ by $2.1387$. $A = 31000\times2.1387=66299.7$.

Answer:

$66299.70$