compounding - solve for future value\nquestion\nisaac invested $4,300 in an account paying an interest rate…
compounding - solve for future value\nquestion\nisaac invested $4,300 in an account paying an interest rate of 5.3% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 6 years?\nanswer\nattempt 1 out of 2\nsubmit answer
Answer
Explanation:
Step1: Recall continuous - compounding formula
The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $t$ is the time in years, and $A$ is the future value of the investment. Here, $P=$4300$, $r = 0.053$ (since $5.3%=0.053$), and $t = 6$.
Step2: Substitute values into the formula
$A=4300\times e^{0.053\times6}$. First, calculate the exponent: $0.053\times6 = 0.318$. Then, find the value of $e^{0.318}$. Using a calculator, $e^{0.318}\approx1.3747$. Now, $A = 4300\times1.3747$. $A=4300\times1.3747 = 5901.21$.
Step3: Round to the nearest hundred dollars
Rounding $5901.21$ to the nearest hundred dollars, we look at the tens - digit. Since the tens - digit is 0, $A\approx5900$.
Answer:
$5900$