jana invests a sum of money in a retirement account with a fixed annual interest rate of 2.15% 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. We are given that $A=$1912.41$, $r = 0.0215$ (since $2.15%=0.0215$), and $t = 10$. We need to solve the formula $A = Pe^{rt}$ for $P$.

Step2: Rearrange the formula for $P$

Dividing both sides of the equation $A = Pe^{rt}$ by $e^{rt}$, we get $P=\frac{A}{e^{rt}}$.

Step3: Substitute the given values

Substitute $A = 1912.41$, $r=0.0215$, and $t = 10$ into the formula $P=\frac{A}{e^{rt}}$. First, calculate $e^{rt}=e^{0.0215\times10}=e^{0.215}$. Using a calculator, $e^{0.215}\approx1.24$. Then $P=\frac{1912.41}{e^{0.215}}=\frac{1912.41}{1.24}\approx1542.27$.

Answer:

$1542.27$