in 1 year, cora wants to buy a bicycle that costs $800.00. if she opens a savings account that earns 13%…

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 know that $A=$800$, $r = 0.13$, and $t = 1$. 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

Substitute $A = 800$, $r=0.13$, and $t = 1$ into the formula $P=\frac{A}{e^{rt}}$. We get $P=\frac{800}{e^{0.13\times1}}=\frac{800}{e^{0.13}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.13}\approx1.13940$, and $P=\frac{800}{1.13940}\approx702.12$.

Answer:

$702.12$