tina opened a savings account and deposited $689.00 as principal. the account earns 9% interest, 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 amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, $P=$689$, $r = 0.09$ (since $9%=0.09$), and $t = 7$.

Step2: Calculate the final amount $A$

Substitute the values into the formula: $A=689\times e^{0.09\times7}$. First, calculate the exponent: $0.09\times7 = 0.63$. Then, find $e^{0.63}\approx1.8776$. So, $A = 689\times1.8776\approx1293.67$.

Step3: Calculate the interest earned

The interest earned $I$ is the final amount minus the principal amount. So, $I=A - P$. Substitute $A\approx1293.67$ and $P = 689$ into the formula: $I=1293.67-689=$604.67$.

Answer:

$604.67$