addison is going to invest in an account paying an interest rate of 6% compounded continuously. how much…

Answer:

$70300$

Explanation:

Step1: Recall continuous - compounding formula

$A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know that $A=$94000$, $r = 0.06$ (since $6%=0.06$), and $t = 5$. We need to solve for $P$.

Step2: Rearrange the formula for $P$

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

Step3: Substitute the values

Substitute $A = 94000$, $r=0.06$, and $t = 5$ into the formula for $P$. $P=\frac{94000}{e^{0.06\times5}}=\frac{94000}{e^{0.3}}$. We know that $e^{0.3}\approx1.34986$.

Step4: Calculate $P$

$P=\frac{94000}{1.34986}\approx70214.3$. Rounding to the nearest ten dollars, $P\approx70300$.