luis invested $62,000 in an account paying an interest rate of 3% compounded continuously. assuming no…

Explanation:

Step1: Recall 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: Identify the values of $P$, $r$, and $t$

Given that $P=$62000$, $r = 0.03$ (since $3%=0.03$), and $t = 16$ years.

Step3: Substitute the values into the formula

$A=62000\times e^{0.03\times16}$. First, calculate the exponent: $0.03\times16 = 0.48$. Then, find the value of $e^{0.48}$. Using a calculator, $e^{0.48}\approx1.616074$. Now, multiply by the principal: $A = 62000\times1.616074$. $A\approx62000\times1.616074 = 100196.588$.

Step4: Round to the nearest dollar

Rounding $100196.588$ to the nearest dollar gives $A\approx100197$.

Answer:

$100197$