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

you win $12,000 in the lottery. you decide to deposit the money in a savings account until you graduate from college in 7 years. your bank can give you an interest rate of 7.5% compounded continuously. how much will you have in your account after 7 years? round your answer to the nearest cent (hundredth)

you win $12,000 in the lottery. you decide to deposit the money in a savings account until you graduate from college in 7 years. your bank can give you an interest rate of 7.5% compounded continuously. how much will you have in your account after 7 years? round your answer to the nearest cent (hundredth)

Answer

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.

Step2: Identify the values of $P$, $r$, and $t$

$P=$12000$, $r = 0.075$ (since $7.5%=0.075$), and $t = 7$ years.

Step3: Substitute the values into the formula

$A=12000\times e^{0.075\times7}$. First, calculate the exponent: $0.075\times7 = 0.525$. Then, find $e^{0.525}$. Using a calculator, $e^{0.525}\approx1.69045$. Multiply by the principal: $A = 12000\times1.69045=20285.4$.

Answer:

$$20285.40$