question 1\nyou deposit $6000 in an account earning 8% interest compounded continuously. how much will you…

question 1\nyou deposit $6000 in an account earning 8% interest compounded continuously. how much will you have in the account in 10 years?\n*\nalgebraic work must be shown to retain points on quizzes, midterm or final\nquestion help: video post to forum\nsubmit question\nquestion 2\nhow much money would be in an account if $6,000 is deposited at 7% interest compounded continuously and the money is left for 5 years?\nquestion help: video post to forum\nsubmit question\nquestion 3\nhow much would you need to deposit in an account now in order to have $2,000 in the account in 10 years if the account earns 8% interest compounded continuously?\nquestion help: video post to forum\nsubmit question

question 1\nyou deposit $6000 in an account earning 8% interest compounded continuously. how much will you have in the account in 10 years?\n*\nalgebraic work must be shown to retain points on quizzes, midterm or final\nquestion help: video post to forum\nsubmit question\nquestion 2\nhow much money would be in an account if $6,000 is deposited at 7% interest compounded continuously and the money is left for 5 years?\nquestion help: video post to forum\nsubmit question\nquestion 3\nhow much would you need to deposit in an account now in order to have $2,000 in the account in 10 years if the account earns 8% interest compounded continuously?\nquestion help: video post to forum\nsubmit question

Answer

Question 1

Explanation:

Step1: Identify the 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. Here, $P = 6000$, $r=0.08$, and $t = 10$.

Step2: Substitute values into the formula

$A=6000\times e^{0.08\times10}=6000\times e^{0.8}$.

Step3: Calculate the value

Using a calculator, $e^{0.8}\approx2.22554$, so $A = 6000\times2.22554 = 13353.24$.

Answer:

$13353.24$

Question 2

Explanation:

Step1: Identify the formula

Use the continuous - compounding formula $A = Pe^{rt}$. Here, $P = 6000$, $r = 0.07$, and $t=5$.

Step2: Substitute values into the formula

$A=6000\times e^{0.07\times5}=6000\times e^{0.35}$.

Step3: Calculate the value

Using a calculator, $e^{0.35}\approx1.41907$, so $A=6000\times1.41907 = 8514.42$.

Answer:

$8514.42$

Question 3

Explanation:

Step1: Identify the formula

The continuous - compounding formula is $A = Pe^{rt}$, and we want to find $P$. Rearranging the formula for $P$ gives $P=\frac{A}{e^{rt}}$. Here, $A = 2000$, $r = 0.08$, and $t = 10$.

Step2: Substitute values into the formula

$P=\frac{2000}{e^{0.08\times10}}=\frac{2000}{e^{0.8}}$.

Step3: Calculate the value

Since $e^{0.8}\approx2.22554$, then $P=\frac{2000}{2.22554}\approx898.65$.

Answer:

$898.65$