if your interest rate is 4.5% compounding con...
if your interest rate is 4.5% compounding continuously, how much money do you have if you invest $1000 for 10 years (round to the nearest penny)?
Answer
# Explanation:
## Step1: Recall continuous - compounding formula
The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.
## Step2: Convert the interest rate to decimal
Given $r = 4.5\%=0.045$, $P = 1000$, and $t = 10$.
## Step3: Substitute values into the formula
$A=1000\times e^{0.045\times10}$.
## Step4: Calculate the exponent
$0.045\times10 = 0.45$. So $A = 1000\times e^{0.45}$.
## Step5: Evaluate $e^{0.45}$ and find $A$
Using a calculator, $e^{0.45}\approx1.568312$. Then $A = 1000\times1.568312=1568.312$.
## Step6: Round to the nearest penny
Rounding $1568.312$ to the nearest penny gives $A\approx1568.31$.
# Answer:
$1568.31$