sue earned some money doing odd jobs last summer and put it in a savings account that earns 13% interest…

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 (initial amount), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know that $A=$2878$, $r = 0.13$, and $t = 4$. We need to solve for $P$.

Step2: Rearrange the formula to solve for $P$

Starting with $A = Pe^{rt}$, we can isolate $P$ by dividing both sides of the equation by $e^{rt}$. So, $P=\frac{A}{e^{rt}}$.

Step3: Substitute the given values into the formula for $P$

Substitute $A = 2878$, $r=0.13$, and $t = 4$ into the formula $P=\frac{A}{e^{rt}}$. We have $e^{rt}=e^{0.13\times4}=e^{0.52}$. Using a calculator, $e^{0.52}\approx1.68201$. Then $P=\frac{2878}{1.68201}\approx1711.05$.

Answer:

$1711.05$