Question

jerome will be buying a used car for $11,000 in 4 years. how much money should he ask his parents for now so that, if he invests it at 9% compounded continuously, he will have enough to buy the car?
jerome should ask for $\square$.
(round to the nearest cent as needed.)

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. We need to find $P$ when $A = 11000$, $r = 0.09$ (since 9% = 0.09), and $t = 4$. Rearranging the formula to solve for $P$ gives $P=\frac{A}{e^{rt}}$.

Step2: Substitute the given values into the formula

First, calculate $rt$: $rt = 0.09\times4 = 0.36$. Then, calculate $e^{0.36}$. We know that $e\approx2.71828$, so $e^{0.36}\approx2.71828^{0.36}\approx1.433329$. Now, substitute $A = 11000$ and $e^{rt}\approx1.433329$ into the formula for $P$: $P=\frac{11000}{1.433329}\approx7674.23$.

Answer:

$\boxed{7674.23}$