jerome will be buying a used car for $9,000 i...
jerome will be buying a used car for $9,000 in 4 years. how much money should he ask his parents for now so that, if he invests it at 3% compounded continuously, he will have enough to buy the car? jerome should ask for $ (round to the nearest cent as needed.)
Answer
# Answer:
$7972.58$
# Explanation:
## Step1: Recall continuous - compounding formula
The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We want to find $P$, and we know that $A=\$9000$, $r = 0.03$, and $t = 4$. Rearranging the formula for $P$ gives $P=\frac{A}{e^{rt}}$.
## Step2: Substitute values into the formula
Substitute $A = 9000$, $r=0.03$, and $t = 4$ into the formula $P=\frac{A}{e^{rt}}$. So $P=\frac{9000}{e^{0.03\times4}}$.
## Step3: Calculate the exponent
First, calculate $0.03\times4=0.12$. Then $e^{0.12}\approx1.127497$.
## Step4: Calculate the principal amount
$P=\frac{9000}{1.127497}\approx7972.58$.