a certain loan program offers an interest rate of 9% per year, compounded continuously. assuming no payments…

Explanation:

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

Given that $P=$1800$, $r = 0.09$ (since $9%=0.09$), and $t = 4$ years.

Step3: Substitute the values into the formula

$A=1800\times e^{0.09\times4}$. First, calculate the exponent: $0.09\times4 = 0.36$. Then, find the value of $e^{0.36}$. Using a calculator, $e^{0.36}\approx1.433329$. Now, multiply by the principal: $A = 1800\times1.433329=2580.0$.

Answer:

$$2580.00$