how much money must you invest now at 4.8% interest compounded continuously in order to have $10,000 at the…

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 need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{e^{rt}}$.

Step2: Convert the interest rate to decimal form

The annual interest rate $r = 4.8%=0.048$, $A = 10000$, and $t = 6$.

Step3: Substitute the values into the formula

$P=\frac{10000}{e^{0.048\times6}}$. First, calculate the exponent: $0.048\times6 = 0.288$. Then, find $e^{0.288}$. Using a calculator, $e^{0.288}\approx1.3337$. So, $P=\frac{10000}{1.3337}\approx7509.19$.

Answer:

$7509.19$