in 2 years, quinn wants to buy a bicycle that costs $600.00. if he opens a savings account that earns 4%…

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 want to find $P$, and we know that $A=$600$, $r = 0.04$ (since $4%=0.04$), and $t = 2$. Rearranging the formula for $P$ gives $P=\frac{A}{e^{rt}}$.

Step2: Substitute values

Substitute $A = 600$, $r=0.04$, and $t = 2$ into the formula $P=\frac{A}{e^{rt}}$. So $P=\frac{600}{e^{0.04\times2}}=\frac{600}{e^{0.08}}$.

Step3: Calculate the value

We know that $e^{0.08}\approx1.083287$. Then $P=\frac{600}{1.083287}\approx554.74$.

Answer:

$554.74$