danielle inherited some money from her grandfather and put it in a bank account that earns 6% interest…

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. Here, $A=$1432$, $r = 0.06$, and $t = 1$. We need to find $P$ first. $A=Pe^{rt}\Rightarrow P=\frac{A}{e^{rt}}$

Step2: Calculate the principal amount $P$

Substitute the values into the formula: $P=\frac{1432}{e^{0.06\times1}}$. Since $e^{0.06}\approx1.061836546$, then $P=\frac{1432}{1.061836546}\approx1348.66$.

Step3: Calculate the interest earned

The interest earned $I$ is the difference between the final amount $A$ and the principal amount $P$. So $I=A - P$. Substitute $A = 1432$ and $P\approx1348.66$ into the formula: $I=1432-1348.66 = 83.34$.

Answer:

$83.34$