if you deposit $750 in an account that pays 8...
if you deposit $750 in an account that pays 8% annual interest compounded continuously, what will the balance be after five years?\n\na. $29,803.91\nb. $1,277.16\nc. $1,832.06\nd. $1,118.87
Answer
# Answer:
B. $\$1,277.16$
# Explanation:
## Step1: Identify the 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: Convert the interest rate
Given $r = 8\%=0.08$, $P=\$750$, and $t = 5$ years.
## Step3: Substitute values into the formula
$A=750\times e^{0.08\times5}$.
## Step4: Calculate the exponent
$0.08\times5 = 0.4$. So, $A = 750\times e^{0.4}$.
## Step5: Find the value of $e^{0.4}$
Using a calculator, $e^{0.4}\approx1.4918247$.
## Step6: Calculate the final amount
$A=750\times1.4918247\approx1277.16$.