how much money must you invest now at 4.6% 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 (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

The annual interest rate $r = 4.6%=0.046$, $A = 10000$, and $t = 5$.

Step3: Substitute values into the formula

$P=\frac{10000}{e^{0.046\times5}}$. First, calculate the exponent: $0.046\times5 = 0.23$. Then, find $e^{0.23}$. Using a calculator, $e^{0.23}\approx1.2586$. So, $P=\frac{10000}{1.2586}\approx7945.22$.

Answer:

$7945.22$