you win $12,000 in the lottery. you decide to deposit the money in a savings account until you graduate from…

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal form

The given interest rate is $7.5%$. To convert it to decimal form, we divide by 100. So, $r=0.075$. The principal amount $P = 12000$ and the number of years $t = 7$.

Step3: Substitute the values into the formula

Substitute $P = 12000$, $r=0.075$, and $t = 7$ into the formula $A = Pe^{rt}$. We get $A=12000\times e^{0.075\times7}$.

Step4: Calculate the exponent part

First, calculate $0.075\times7 = 0.525$. Then, find the value of $e^{0.525}$. Using a calculator, $e^{0.525}\approx1.690458$.

Step5: Calculate the final amount

Multiply 12000 by $e^{0.525}$. So, $A = 12000\times1.690458=20285.496$.

Step6: Round the answer

Rounding to the nearest cent, $A\approx20285.50$.

Answer:

$20285.50$