how much would you have to deposit in an account with a 9% interest rate, compounded continuously, to have…

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 deposit), $r$ 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 and identify values

The annual interest rate $r = 9%=0.09$, the final amount $A = 1500$, and the time $t = 5$ years.

Step3: Substitute values into the formula

$P=\frac{1500}{e^{0.09\times5}}$. First, calculate the exponent: $0.09\times5 = 0.45$. Then, find $e^{0.45}\approx1.56831$. So, $P=\frac{1500}{1.56831}\approx956.44$.

Answer:

$956.44$