john invests a sum of money in a retirement account with a fixed annual interest rate of 5.35 % compounded…

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 (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $A=$15265.07$, $r = 0.0535$ (since $5.35%=0.0535$), and $t = 5$ years. We need to solve for $P$.

Step2: Rearrange the formula 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

Substitute $A = 15265.07$, $r=0.0535$, and $t = 5$ into the formula for $P$. We have $P=\frac{15265.07}{e^{0.0535\times5}}$. First, calculate the exponent: $0.0535\times5=0.2675$. Then, find $e^{0.2675}\approx1.3069$. Now, $P=\frac{15265.07}{1.3069}\approx11680$.

Answer:

$11680$