Question

jackson invested $8,200 in an account paying an interest rate of 4% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 8 years?

Explanation:

Step1: Write the 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), and $t$ is the time in years.

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

Given that $P=\$8200$, $r = 0.04$ (since $4\%=0.04$), and $t = 8$ years.

Step3: Substitute the values into the formula

Substitute $P = 8200$, $r=0.04$, and $t = 8$ into $A=Pe^{rt}$:
$A=8200\times e^{0.04\times8}=8200\times e^{0.32}$

Step4: Calculate the value of $e^{0.32}$

Using a calculator, $e^{0.32}\approx1.37712776$

Step5: Multiply to find $A$

$A = 8200\times1.37712776\approx11364$

Answer:

$11364$