a wedding photographer has been saving money to use for travel during retirement. the photographer plans to…

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. We need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{e^{rt}}$.

Step2: Identify the values of $A$, $r$, and $t$

We are given that $A = 40000$, $r=0.047$ (since $4.7%=0.047$), and $t = 20$.

Step3: Substitute the values into the formula

$P=\frac{40000}{e^{0.047\times20}}$. First, calculate the exponent: $0.047\times20 = 0.94$. Then, find $e^{0.94}\approx2.5607$. So, $P=\frac{40000}{2.5607}\approx15620.71$.

Answer:

$$15620.71$