how much would you have to deposit in an account with a 4.75% interest rate, compounded continuously, to…

Explanation:

Step1: Recall the continuous - compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We are given that $A=$20000$, $r = 0.0475$ (since $4.75%=0.0475$), and $t = 20$. We need to solve for $P$. From $A = Pe^{rt}$, we can rewrite it as $P=\frac{A}{e^{rt}}$.

Step2: Substitute the values into the formula

Substitute $A = 20000$, $r=0.0475$, and $t = 20$ into the formula $P=\frac{A}{e^{rt}}$. We get $P=\frac{20000}{e^{0.0475\times20}}$. First, calculate the exponent: $0.0475\times20 = 0.95$. Then, $e^{0.95}\approx2.58563$. So, $P=\frac{20000}{2.58563}$.

Step3: Calculate the value of $P$

$P=\frac{20000}{2.58563}\approx7735.07$.

Answer:

$7735.07$